Find consecutive Powers, i.e., solutions to

excluding 0 and 1. Catalan's Conjecture is 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.

© 1996-9

1999-05-26