the abc conjecture

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the abc conjecture

Postby phillip1882 » Thu Oct 30, 2014 2:39 am UTC
so some interesting properties i wanted to point out...
proving that the number of exceptions is infinite when k = 1 is easy.
let a = 1 and c = 9^n where n is any whole number.
this always results in a rad(a*b*c) that is less than c.
another cool property is using primative pythagoeran triples.
let m^2 -n^2, 2*m*n, m^2 +n^2 = d,e,f where gcd(m,n) = 1 and ether 2|m or 2|n.
then a likely exception is (d-e)^2, 4*d*e, (d+e)^2 or (f-e)^2, 4*f*e, (f+e)^2. just thought i'd throw these juicy tidbits out there for anyone interested in the problem.
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