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

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

2003-01-07

arxiv.org/abs/math/0301050v1

Mathematics

Number Theory

9 pages

Scientific paper

We prove that for any positive integer c there are at least N(c), $1\leq N(c)
< \phi(c)/2$ 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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