The abc-conjecture is true for at least $N(c),1\le N(c)<\varphi (c)\mathrm{/}2$, partitions a, b of c

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