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One formulation of the abc-conjecture is: $$\forall a,b \in \mathbb{N}: \frac{a+b}{\gcd(a,b)}< \operatorname{rad}\left ( \frac{ab(a+b)}{\gcd(a,b)^3}\right )^2 $$ Let us define: $$K(a,b) := \frac{2(...

We did some statistics about the 14 million good abc triples below 10^18 taken from Bart de Smith site. This was examining just the top of the iceberg, since the interesting triples grow very likely ...