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Catalan's Diophantine Problem

Find consecutive Powers, i.e., solutions to

\begin{displaymath}
a^b-c^d=1,
\end{displaymath}

excluding 0 and 1. Catalan's Conjecture is that the only solution is $3^2-2^3=1$, so 8 and 9 ($2^3$ and $3^2$) are the only consecutive Powers (again excluding 0 and 1).

See also Catalan's Conjecture


References

Cassels, J. W. S. ``On the Equation $a^x-b^y=1$. II.'' Proc. Cambridge Phil. Soc. 56, 97-103, 1960.

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




© 1996-9 Eric W. Weisstein
1999-05-26