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).

See also

Catalan's Conjecture

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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 Problem

Cite this as:

Weisstein, Eric W. "Catalan's Diophantine Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CatalansDiophantineProblem.html

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