S Smith May 2010 10 0 May 18, 2010 #1 Prove that the ABC conjecture implies there exists only finitely many triples of consecutive powerful numbers (Hint: Apply ABC to (n^2 - 1) + 1 = n^2, and note N(n^2(n^2 - 1)) <= n^(3/2) )
Prove that the ABC conjecture implies there exists only finitely many triples of consecutive powerful numbers (Hint: Apply ABC to (n^2 - 1) + 1 = n^2, and note N(n^2(n^2 - 1)) <= n^(3/2) )