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

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

2005-11-09

arxiv.org/abs/math/0511224v3

Mathematics

Number Theory

14 pages The proof of Theorem 2 in the initial paper is erroneus. In the replacement paper, Theorems 3 and 4 give a correct pr

Scientific paper

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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