For the discussion of math. Duh.

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Phi(x) of all those numbers is equal to 160
187
205
328
352
374
400
410
440
492
528
600
660

Why?

Imagine that you have to factorize 187 and you know that 400 which is easy to factorize has its Euler totient such as phi(187)=phi(400) then you factorize 187 easily.
That is just one hint to approximate any semiprime. There are others to discover.

gmalivuk
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Wikipedia is a fine place to reference for very basic mathematical ideas, such as the definition of identity. If you don't know what a mathematical identity is, then you are not in a position to reject WIkipedia because it contains occasional errors.

The reason to reject your equation because it's an identity, is that identities are true for all values of the variables, and so they don't tell us any information about those variables.

x^2 - y^2 = (x+y)*(x-y) is an identity. It tells us about a (useful) relationship between expressions, but it tells us nothing about x or y.
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gmalivuk wrote:Wikipedia is a fine place to reference for very basic mathematical ideas, such as the definition of identity. If you don't know what a mathematical identity is, then you are not in a position to reject WIkipedia because it contains occasional errors.

The reason to reject your equation because it's an identity, is that identities are true for all values of the variables, and so they don't tell us any information about those variables.

x^2 - y^2 = (x+y)*(x-y) is an identity. It tells us about a (useful) relationship between expressions, but it tells us nothing about x or y.

Is this an identity? yes or no.

A(A-y+1) mod (p*q-2)=A-(2*y)+4

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Each one here and elsewhere has the right to have his point of view about Wikipedia.
No one has the right to tell me what I have to think about Wikipedia no matter who he is.

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How do you know what is useful and what is not when you do not know what I will do with such unuseful identity in your point of view?

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Please stop triple-posting. You can edit your last post if it's still the most recent post in a thread.

If an identity tells you nothing about a variable, then it doesn't tell you anything useful about that variable.

Goahead52 wrote:Is this an identity? yes or no.

A(A-y+1) mod (p*q-2)=A-(2*y)+4

Yes, that is an identity. Cauchy already explained why it's an identity.

Because it's an identity, it tells us nothing about the values of A or y.
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gmalivuk wrote:Please stop triple-posting. You can edit your last post if it's still the most recent post in a thread.

If an identity tells you nothing about a variable, then it doesn't tell you anything useful about that variable.

How do you know that the same variable could be written differently using even external variables?
You did not answer to my question directly.
Is it an identity? yes or no.
This identity tells me lot that you can not even imagine.

It is not because you are moderator that you are going to impose your views.
So please stop playing the teacher.
I`m not an alumni.
Why are you assuming that the basic ideas in mathematics are not false?

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Definitions are not false. They are definitions. They can't be false, because that is not how definitions work.

The statement "A(A-y+1) mod (A-2)=A-(2*y)+4" is true for all A and all y. It therefore can tell us nothing about A or about y, just like "x=x" tells us nothing about the value of x.
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gmalivuk wrote:Definitions are not false. They are definitions. They can't be false, because that is not how definitions work.

The statement "A(A-y+1) mod (A-2)=A-(2*y)+4" is true for all A and all y. It therefore can tell us nothing about A or about y, just like "x=x" tells us nothing about the value of x.

So if x=(a+b)^2
and x-a^2+2ab+b^2
is then going to tell you something?

A definition is not universal.
For each problem a mathematician can his own definition different from the community. All depending on what he intend to prove.
How many mathematical definitions are still controversial? until today.
Lot.
The definition is just a convention. Some people agree to name the infinite as they wish.
That`s it.
Mathematics is just a language built by community for some reasons.
Solving mathematical problems does not need to bow to the community and its language.
It does even need to know the basics.

Demki
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gmalivuk wrote:Please stop triple-posting. You can edit your last post if it's still the most recent post in a thread.

If an identity tells you nothing about a variable, then it doesn't tell you anything useful about that variable.

How do you know that the same variable could be written differently using even external variables?
You did not answer to my question directly.
Is it an identity? yes or no.
This identity tells me lot that you can not even imagine.

It is not because you are moderator that you are going to impose your views.
So please stop playing the teacher.
I`m not an alumni.
Why are you assuming that the basic ideas in mathematics are not false?

The only time he "imposed" something on you as a moderator is when he told you not to triple post, and when he merged your threads, both are beneficial to the rest of us, and don't really hinder whatever you are trying to do.
Yes, it is an identity, as Cauchy has shown.

As for your latest post: if you ask someone what an identity is, without providing your definition of identity, that person has to assume the standard definition of identity, as gmalivuk did.
Also, what do you mean by "So if x=(a+b)^2
and x-a^2+2ab+b^2"?
"x-a^2+2ab+b^2" is not a statement, but an expression, so you can't just use logical connectives with it.

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Here is what he said :
"If you don't know what a mathematical identity is, then you are not in a position to reject WIkipedia because it contains occasional errors."

It said it all!
The teacher talking to alumnis.
I`m not an alumni.
I know wikipedia since the beginning and I have seen many absurdities! in mathematics.
Now they have lot of collaborators.

Cauchy says it is an identity and the moderator said no on the same thread.
I prefer not even to post.
I will keep everything for me and that`s it.
Good luck to everybody.

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Goahead52 wrote:Cauchy says it is an identity and the moderator said no on the same thread.

gmalivuk wrote:Yes, that is an identity. Cauchy already explained why it's an identity.

...?

Also, just looking at it from a Bayesian perspective, which of these things is more likely?

A) You have completely overturned and revolutionized the very foundations of mathematics, including rendering most of modern cryptography totally obsolete, with an idea so concise and profound that it can easily be expressed via a forum post (and you don't have a better venue in which to post it), but which nobody else has come up with over the past several decades despite exceedingly strong incentives for breaking cryptography.

B) You're misunderstanding something somewhere, as many people have done in the past and many people will do in the future.

Does this tilt any further in one direction if we update our priors based on the fact that you seem to either not know, or not accept, standard mathematical terminology/definitions?
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Goahead52 wrote:Cauchy says it is an identity and the moderator said no on the same thread.
Where did I say that?

I understand that English isn't your first language, so misunderstandings can happen sometimes, but I can't see where you think I said it wasn't an identity.
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It is not about mastering English or no.
The difference between an identity and an equation is meaningless.
y=y is apparently an identity.
It show you "nothing" but all depend on what you are going to put on y.
y could be represent an infinite number of ways.
Any equation no matter how complex is it either some some values or all the values will end as identity.
Making the distinction between an identity and equation is just a convention like encrypted code.
I said that I`m too tired and sick to simplify my formula even it was simple.
Why because I had in mind not the simplification but what I need to put on the variable y.
I have many ways to build y so until now I still do not know which way I have to choose such as the solution could be easy to reach.
I was upset about what you said about Wikipedia. Wikipedia lack of credibility even when it comes to the basics in mathematics.
So please if you take Wikipedia as reference that is your choice not mine.
In mathematics and in many other fields the basics are almost imposed by the communities. Like Oxford Dictionaries and others dictionaries (Larousse, Robert, Littre etc.. in french).
All depends on what you are trying to solve. Definitions are required to be as precise as possible. It is a question of mutual understanding. If the definition you give is in contradiction of what you need to prove then the debate will focus on the definition. But as long as it does not change your proof anyone will accept it. The perfect clarity of the definition itself is not mandatory. If you talk to non biologist you are going to give a precise definition of what is a cell. We are here in a forum with 1000`s of levels (not 1 or 2) because each one of the members is assumed to have some knowledge in mathematics. The goal is not to be understood by professionals. The goal to be understood by the majority. No one should act as teacher even if he is professional teacher in real life. If you feel that someone does not know the basics (or what you are assuming as basics) give your own definition of that basics. What you mean by identity what you mean by equation but do not ever tell him you do not know the basics go to Wikipedia.
Anyway good luck to you all.
I will finish my job alone without sharing with anyone.
Mathematics are ideas before becoming technical methods.
The fields have a lot of technicians but few imaginative guys and woman able to see beyond technical matters.
The progress in mathematics is linked to the imaginative ability not to technical matters. Creating new concepts, moving to new approaches etc...that is what is needed. Bashing others because hundreds of mathematicians failed is just a sign of frustration among those who consider themselves as masters.

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y=y does *not* depend on y, that's what makes it an identity. You can put *anything* for y and it will still be true, because that's how '=' works. It tells us something about '=', but it doesn't tell us anything about y.

y=x, on the other hand, is not an identity. It's not true for all possible values of y and, independently, all possible values of x. If y=3, then we know instantly that x=3. The *equation* y=x tells us information we didn't already have, and we can use it with other information to get useful results.

Your identity is slightly more complex, but it still doesn't tell us anything about the variables in it.

You can complain all you want about how you don't like making the distinction, but everyone else in the world would like to have a way of saying that a formula does or doesn't give us any new information. So we're going to keep making a distinction, and the identity you wrote is going to keep being on the "no new information" side of that distinction.

(You don't have to accept everyone else's definitions to do math on your own, but you do need to at least understand our definitions if you want to communicate with us.)
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PeteP
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Any equation no matter how complex is it either some some values or all the values will end as identity.

Based on that sentences my best guess is that you are thinking values that fulfill the equation are identities or something? Values don't end up as identity, identity refers to the equation itself.

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and x-a^2+2ab+b^2
is then going to tell you something?

x = (a+b)^2 is not an identity: if x = 2, a = 1 and b = 3, it's clearly false. So if you assert that it's true, you find out something about x, a and b. That's why x-(a^2+2ab+b^2) can be evaluated to 0, under the premise that the equation is true.

Loosely:

An expression is something that evaluates to a number, like 2+2 or 4(3^2-5). It's possible that an expression has one or more variables in it, like 2x+y or (a+b)^2 or even just x, in which case the expression evaluates to a number after a value has been substituted for each variable (with all instances of the same variable receiving the same value).

An equation is a sentence of the form <expression1> = <expression2>, where <expression1> and <expression2> can be any expressions. Examples are 2+2 = 4, 2+2 = 5, and x^2 = 17. For any substitution of values into variables, the equation is either true of false, depending on whether the two expressions evaluate to the same number or not.

An identity is a special type of equation that's true for any assignment of values to variables. 2+2 = 4 is an identity; 2+2 = 5 is not. (a+b)^2 = a^2+2ab+b^2 is an identity; x = (a+b)^2 is not.
(Some people might say that an identity is not an equation, but that exclusion seems meaningless to me.)

You're free to use whatever definitions you'd like, but these are the ones we use. If you're not using these definitions, then either a) you need to say what your new definitions are, or b) you won't be properly understood.

Under our definitions, stating that an equation is true in general can tell you information about the variables in the equation, either their possible values or relationships between them. If I say that x^2 = 16, then x is restricted to two possible values, and if I say that x = (a+b)^2, this imposes a relationship between x, a, and b. But stating that an identity is true can't tell you any information about the variables, because the identity is true no matter what value the variables have. I can already solve your identity for y: y can be anything regardless of what A is, because no matter what y and A are, the identity is true. No possibilities have been thrown out, so we gain no new information.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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The sum 1+9+9^2+9^3+9^4...+9^k is always a triangular number
Is it an identity or an equation?
Thank you for any comment.

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Goahead52 wrote:The sum 1+9+9^2+9^3+9^4...+9^k is always a triangular number
Is it an identity or an equation?
Thank you for any comment.

According to the definitions, that is neither, because you're not saying (expression 1) = (expression 2).

You could say that, for all natural numbers k, there is a natural number n such that
1 + 9 +...+ 9^k = n(n+1)/2

Then you're saying there are values for which that equation is true, though you're still not saying anything interesting about the variables k or n, because it's true for all k and you're just saying there exists some n.

No one is saying identities are useless, we' re just saying they don't (and cannot possibly) tell you information about the *variables* in the expressions.
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If I replace n by something related to 9 and its powers it will become an identity.
You will learn nothing from it.
In my point of view the distinction between identity and equation is meaningless when it comes to solving any problem.
Many distinctions are unhelpful when it comes to attacking a problem.
It add you nothing to know the difference. Waste of time.
I do not even care about what mathematician label this or that. The more important is the result. Once you have the result there is a need to communicate this result to others. Then and only then you need clarity. Not before. Because many things happens in your brain that you are maybe the only one to know where you are heading to and what you want to achieve.
Now things become clearer about the factorization in my mind.
We could reduce this problem to a linear congruence problem.

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The following is an identity - it is true for all (real) x:
sin2(x) + cos2(x) = 1
This is a useful identity, but it places no constraints on x.

The following is not an identity - it is not true for all x.
sin(x) + cos(x) = 1
This equation tells us x is an integer multiple of pi/2.

PeteP
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Goahead52 wrote:If I replace n by something related to 9 and its powers it will become an identity.
You will learn nothing from it.

Out of curiosity, could you do so please?

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PeteP wrote:
Goahead52 wrote:If I replace n by something related to 9 and its powers it will become an identity.
You will learn nothing from it.

Out of curiosity, could you do so please?

You can do it by yourself just by finding n.
You surely know how to sum geometric sequence. Hence it will be done in few seconds.
Anyway I developed an algorithm to sum any sequence. Even the sum of the prime numbers.
Each sequence could be represented in thousand of forms (I mean closed formulas).
Anyway I do not know the basics of mathematics and I will rely on Wikipedia as it was advised.
I have one year to master their basics.
Without knowing the basics in one I could produce at least 1000 of mathematical results as I`m sick and too ill.

PeteP
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To be more direct, I am asking because I am still unsure whether you understand what an identity is so I wanted to see how you would go about turning it into an identity.

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Knowing what is an identity as I said will not help me to solve any problem.
When things are not really helpful it is simple : I ignore them.
You know what is an identity and what is an equation good for you. Fine! you are serious mathematician with huge knowledge I do not even discuss it. Does this help you to solve a problem like giving a closed formula of the number of primes less than n? no!
It helps you to know what was done. That`s it.
I do not want to know what was done deeply in that problem.
In fact I do not care.
I prefer to start from what I know first (few). But with using only few you could recognize a good chief (cooking). A good chief does need a lot of ingredients to make a good meal.
I`m good chief too for myself and my family friends etc...

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You apparently still don't know what an identity is, so you can't say whether knowing would help you.

The names aren't important, the reason for making the distinction is:
"sin(x)^2 + cos(x)^2 = 1" is an interesting and useful identity, which helps us simplify and better understand a lot of other expressions, but which *cannot* tell us *any* information about x, because it is true for all x.
"1+9+9^2+...+9^k is a triangular number" is an interesting and useful statement (if true - I haven't checked), but it *cannot* tell us *any* information about k, because it's true for every k.

If you use the first statement to say something about trigonometry, and the second statement to talk about powers of nine and triangular numbers, then they are useful and give useful information. If you try to use the statements to tell us about x or about k, then you have failed to do so because they don't convey any information about x and k.
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Goahead52 wrote:Knowing what is an identity as I said will not help me to solve any problem.

This seems obviously false.

People learn math specifically because it helps them to solve problems. This sort of anti-intellectual statement is really odd, and is probably the result of the craziness that follows. In general, it is probably unwise to assume that the entire field is making up stuff that doesn't matter.

If I remember correctly, there's a related aphorism that goes something like this. A man coming into town for the first time banged his shin upon a gate, and announced that he could see no use for it, and it would be best thrown away. The townsfolk said unto him "Go, and learn it's use. When you can explain what it is for, then perhaps we will allow you to throw it away"

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1+9+9^2+9^3+....+9^k= 1/2* ((3^k)-1)/2)((3^k+1)+1)/2) is true for all the k`s
n=((3^k)-1))/2
Sum geometric sequence is easy. I skipped that part.

I had just replaced n by its value so the equation become a pure identity.

It that correct?

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Tyndmyr wrote:
Goahead52 wrote:Knowing what is an identity as I said will not help me to solve any problem.

This seems obviously false.

People learn math specifically because it helps them to solve problems. This sort of anti-intellectual statement is really odd, and is probably the result of the craziness that follows. In general, it is probably unwise to assume that the entire field is making up stuff that doesn't matter.

If I remember correctly, there's a related aphorism that goes something like this. A man coming into town for the first time banged his shin upon a gate, and announced that he could see no use for it, and it would be best thrown away. The townsfolk said unto him "Go, and learn it's use. When you can explain what it is for, then perhaps we will allow you to throw it away"

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What do you mean "wrong"? It's a story, a parable, and illustrating example. It may be irrelevant, but I don't see how it can be wrong.
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Zohar wrote:What do you mean "wrong"? It's a story, a parable, and illustrating example. It may be irrelevant, but I don't see how it can be wrong.

Is it wrong in the sense that it has nothing to do with our problem.
That`s it.
Irrelevant maybe more appropriate. I`m not an English native.
I speak and read 4 other languages.
I learned English in school for adults during less than 2 years.

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Your English is occasionally weird but generally understandable.

We're talking about your inability or unwillingness to learn how to talk about mathematics with other people. In that context, particularly with regards to the concept of an identity, the analogy is perfect: You think we should throw away the concept because it's useless, but you don't understand it. We think you should learn what it means before you decide we should throw it away.

If you're unwilling to learn how the rest of us understand and use mathematical words, then why are you posting about math on our forum?
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Demki
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Goahead52 wrote:1+9+9^2+9^3+....+9^k= 1/2* ((3^k)-1)/2)((3^k+1)+1)/2) is true for all the k`s
n=((3^k)-1))/2
Sum geometric sequence is easy. I skipped that part.

I had just replaced n by its value so the equation become a pure identity.

It that correct?

No. It is actually
1+9+9^(2)+...+9^(k)=(1/2)((3^(k+1)-1)/2)((3^(k+1)+1)/2)
With n=(3^(k+1)-1)/2

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Demki wrote:
Goahead52 wrote:1+9+9^2+9^3+....+9^k= 1/2* ((3^k)-1)/2)((3^k+1)+1)/2) is true for all the k`s
n=((3^k)-1))/2
Sum geometric sequence is easy. I skipped that part.

I had just replaced n by its value so the equation become a pure identity.

It that correct?

No. It is actually
1+9+9^(2)+...+9^(k)=(1/2)((3^(k+1)-1)/2)((3^(k+1)+1)/2)
With n=(3^(k+1)-1)/2

You are right. Thank you for the correction.
I was talking about the identity-equation when I said is that correct?
I was focused on identity question not on the formula anyway.
Thank you.

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Goahead, I don't think I can advance the conversation about identities vs equations any further than it's gone, I'll leave that up to people who are better at this sort of thing. I'd rather go back to the more important question - how does your equation purport to help factor numbers?

It looks like this is based on the idea that knowing the sum of the factors of A should make it almost trivially easy to find them (for a powerful computer that can process numbers that big in a reasonable time, anyway). But your formula doesn't do that.

Let's take an example - you used 35 earlier, so let's go with that. We all know the factors of 35, and their sum is 12. So:
35 (35-12+1) = 840, 840 mod 33 is 15

35 - 24 + 4 = 15 (15 mod 33 is trivially 15)

Great, it worked!
...

But what if we didn't know the sum, what if we assumed the sum is 10?
35 (35-10+1) mod 33 is 19
35 - 20 + 4 is 19

Great, it's... oh, no.
...

What if we assume y is 0?
35 (35+1) mod 33 is 6
35+4 mod 33 is 6
...

The point here is that your formula would hold no matter what y is, so finding a closed form for y doesn't really matter. This equation tells us nothing about y - it is true independent of what value we assign to y, so we haven't actually learned anything about the sum of the factors of A. Does that make sense?

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What you just said is not wrong.
phi(pq)+(p+q)=pq+1 is the starting point.
As phi(pq)=pq- (p+q)+1+p+q=pq+1 (Eq or identity 1)
If you ckeck all the members it will give nothing!
You remove pq+1 from both sides you remain p+q-(p+q)=0

Here comes what you put inside each variable.

When I wrote :
1+9+9^2+9^3+.....+9^k=n(n+1)/2
you could see that if you assign the value required to n = (3^(k+1)-1)/2
the left side is exactly equal to the right side no matter what is the value of k.

Now reverse the process using the identity(equation) above (Eq or identity 1).
What can you do? I let use your imagination.
How can we make such equality phi(pq)+(p+q)=pq+1 to make sense?
If we know how to approximate phi(pq) then the problem is solved.
If we know to approximate p+q then the problem.
How can we estimate both in parallel such as we find quickly by convergence the 2?
If we reach phi(pq) then we could easily factorize pq. The same idea prevail for p+q.
What are the parameters that I could substract from pq (I do not know p and q) such as I could build an approximation of phi(pq) and p+q? Both are linked.
Yes there is lot of work done before. Otherwise I could not claim what I claimed.
I`m very tired so I have to stop until tomorrow maybe.
Anyone could solve what I claimed. Using only elementary tools.
It is not because 1000 of mathematicians failed that is impossible.
All depends on how you approach the factorization problem.

lorb
Posts: 405
Joined: Wed Nov 10, 2010 10:34 am UTC
Location: Austria

Can you factor this number Goahead? I think if you can, everyone will agree you are brilliant mathematician. If you can't I think its fair to say you are an imposter.

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17969491597941066732916128449573246156367561808012600070888918835531726460341490933493372247868650755230855864199929221814436684722874052065257937495694348389263171152522525654410980819170611742509702440718010364831638288518852689
Please be gracious in judging my english. (I am not a native speaker/writer.)
http://decodedarfur.org/

Posts: 431
Joined: Thu Oct 16, 2014 9:28 am UTC

lorb wrote:Can you factor this number Goahead? I think if you can, everyone will agree you are brilliant mathematician. If you can't I think its fair to say you are an imposter.

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17969491597941066732916128449573246156367561808012600070888918835531726460341490933493372247868650755230855864199929221814436684722874052065257937495694348389263171152522525654410980819170611742509702440718010364831638288518852689

I`m honored to be called imposter because all the Prophets : Moses, Jesus, Muhammad and others were labelled as imposters. Galilee was called imposter and decapitated.
x+y=pq+1
x is phi(pq)
y is p+q

x and y are UNIQUE. They have only ONE value such as x+y=pq+1 (pq+1 is known).

Do you know the reverse engineering?
I practice the reverse in mathematics which lead me to many results.
A brilliant mathematician will never wait for crowd to recognize him.
Do you know the huge mathematician who died recently and who cut the ties will all the society?
Do you know him?
Certainly not! Except if you google it as usual.

Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Goahead52 wrote:I`m honored to be called imposter because all the Prophets : Moses, Jesus, Muhammad and others were labelled as imposters. Galilee was called imposter and decapitated.

Beware the Galileo Gambit...

lorb
Posts: 405
Joined: Wed Nov 10, 2010 10:34 am UTC
Location: Austria

lorb wrote:Can you factor this number Goahead? I think if you can, everyone will agree you are brilliant mathematician. If you can't I think its fair to say you are an imposter.

Code: Select all

17969491597941066732916128449573246156367561808012600070888918835531726460341490933493372247868650755230855864199929221814436684722874052065257937495694348389263171152522525654410980819170611742509702440718010364831638288518852689

I`m [bla bla bla]

Can you factor this number? Just answer no, or show the factors.

Goahead52 wrote:Do you know the huge mathematician who died recently and who cut the ties will all the society?
Do you know him?
Certainly not! Except if you google it as usual.

Perelman is alive and well
Please be gracious in judging my english. (I am not a native speaker/writer.)
http://decodedarfur.org/