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A strong "abc-conjecture" for certain partitions a+b of c

Constantin M. Petridi
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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).

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Constantin M. Petridi. 2006-03-01. A strong "abc-conjecture" for certain partitions a+b of c. https://arxiv.org/abs/math/0511224

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