The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 23 32 7, so rad(504) = 2 3 7 = 42.
We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:
For example, (5, 27, 32) is an abc-hit, because:
It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c 1000, with c = 12523.
Find c for c 120000.