Hey guys, writing an essay on the abc conjecture and I have gotten stuck on a proof.
It follows from the abc conjecture that there are only finitely many sets of three consecutive powerful integers. The following link has a proof showing that there are only finitely many sets of three powerful numbers in arithmetic sequence (for any fixed common difference).
Consequences of the abc conjecture
However on the step where they define their abc-triple, a= k^2, b=n(n+2k) and c=(n+k)^2, how do we know they are pairwise coprime?
Any help appreciated - thanks. (Happy)