The difference of the cubes of two non-negative successive integers is a square of an integer.
Find few possible pairs.
How about a general formula or evaluation algorithm
(In reply to re: computer exploration
by Jim Keneipp)
I noticed that too. That near-geometric increase comes from the recursion t(n) = 14*t(n-1) - t(n-2), with starting values t(0)=1, t(1)=13. Taking x^2 = 14x - 1, then x = 7 +/- 4*sqrt. The larger root evaluates to 13.92820322.
Edited on February 27, 2010, 6:56 pm