The abc-conjecture is true for at least N(c), 1 ≤ N(c) <ϕ(c)/2, partitions a, b of c

2003/01/07 by Constantin M. Petridi, Petridi, Constantin M.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0301050

9 pages

arxiv created 2003/01/07 · arxiv updated 2009/11/30

Abstract

We prove that for any positive integer c there are at least N(c), 1≤ N(c) < ϕ(c)/2 representations of c as a sum of two positive integers a, b, with no common divisor, such that the N(c) radicals R(abc) are all greater than kc, where k an absolute constant.

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