Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.7

Perfect Powers With All Equal Digits But One

Omar Kihel
Department of Mathematics
Brock University
St. Catharines, Ontario L2S 3A1
Canada

Florian Luca
Instituto de Matemáticas
Universidad Nacional Autónoma de México
C.P. 58089
Morelia, Michoacán
México

Abstract: In this paper, among other results, we show that for any fixed integer l >= 3, there are only finitely many perfect l-th powers all of whose digits are equal but one, except for the trivial families 10^ln when l >= 3 and 8 . 10³ⁿ if l = 3.

Received October 3 2005; revised version received November 9 2005. Published in Journal of Integer Sequences November 14 2005.