20-Aug-1995

Unsolved Problem 34:

Are there only finitely many perfect squares with just two different nonzero decimal digits?

For example, 38^2=1444, 88^2=7744, 109^2=11881, 173^2=29929, 212^2=44944, 235^2=55225, and 3114^2=9696996.

Reference:

[Guy 1994]
Richard K. Guy, Unsolved Problems in Number Theory, second edition. Springer Verlag. New York: 1994. Page 262.
Squares with Two Different Decimal Digits
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