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).
Catalan's Diophantine Problem
See also
Catalan's ConjectureExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Catalan's Diophantine ProblemCite this as:
Weisstein, Eric W. "Catalan's Diophantine Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalansDiophantineProblem.html