Abc Conjecture

It states:

For any <math> \epsilon > 0 </math> there exists a constant <math> C_{\epsilon} > 0 </math>, such that for every triple of positive integers a, b, c satisfying <math> a + b = c </math> and <math> \gcd(a,b) = 1 </math> we have <math> c < C_{\epsilon} rad(abc)^{1+\epsilon} </math>, where <math> rad(n) </math> is the product of the distinct prime divisors of n.

It is a conjecture and has not yet been proven.

See also:

• greatest common divisor (gcd)

External references:

• http://mathworld.wolfram.com/abcConjecture
• http://www.math.unicaen.fr/~nitaj/abc