Congruence ABC implies ABC
Abstract
The ABC conjecture of Masser and Oesterle' states that if (a,b,c) are coprime integers with a + b + c = 0, then sup(a,b,c) < c_e (rad(abc))^{1+e} for any e > 0. Oesterle' has observed that if the ABC conjecture holds for all (a,b,c) with 16  abc, then the full ABC conjecture holds. We extend that result to show that, for every integer N, the "congruence ABC conjecture" that ABC holds for all (a,b,c) with Nabc implies the full ABC conjecture.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:math/9909098
 Bibcode:
 1999math......9098E
 Keywords:

 Number Theory;
 11D41 (Primary) 11D75 (Secondary)
 EPrint:
 4 pages