Congruence ABC implies ABC

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 N|abc implies the full ABC conjecture.Comment: 4 pages; to appear, Indag. Mat

Somers, Town of and Local 456, International Brotherhood of Teamsters (Somers Highway)

In the Matter of the Impasse Between SOMERS, TOWN OF and LOCAL 456 INTERNATIONAL BROTHERHOOD OF TEAMSTERS (SOMERS HIGHWAY DEPARTMENT) CASE NO. M2002-278. BEFORE: Martin Ellenberg, Esq., Fact-Finde