A strong "abc-conjecture" for certain partitions a+b of c
Number Theory
2007-05-23 v3
Abstract
We prove that for any positive integer c and any s > 0 there are representations of c as a sum a+b of two coprime positive integers a, b, such that the respective radicals are all greater than K(s)R(c)^(1-s)c^2. For the reprasentations in question, this is a stronger result than the abc-conjecture, which postulates that these representations are greater than k(s)c^1/(1+s).
Cite
@article{arxiv.math/0511224,
title = {A strong "abc-conjecture" for certain partitions a+b of c},
author = {Constantin M. Petridi},
journal= {arXiv preprint arXiv:math/0511224},
year = {2007}
}
Comments
14 pages The proof of Theorem 2 in the initial paper is erroneus. In the replacement paper, Theorems 3 and 4 give a correct proof. Misprints in proof of theorem 3 have being corrected, and certain clarifications added