Dan Asimov: Anyway, as Ramanujan is famous for pointing out to Hardy,

9^3 + 10^3 = 12^3 + 1

.

This is a counterexample to Fermat's Last Theorem . . . almost. It's off by one.

QUESTION: Are there other examples of integers x, y, z for which

x^3 + y^3 = z^3 + 1

--see http://www.math.psu.edu/vstein/preprints/Rachel11.ps for a beginning.