Catalan's Diophantine Problem

Find consecutive powers, i.e., solutions to

excluding 0 and 1. Catalan's conjecture states that the only solution is , so 8 and 9 ( and ) are the only consecutive powers (again excluding 0 and 1).

REFERENCES:

Cassels, J. W. S. "On the Equation . II." Proc. Cambridge Phil. Soc. 56, 97-103, 1960.

Inkeri, K. "On Catalan's Problem." Acta Arith. 9, 285-290, 1964.