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x^a - x^b is divisible by n, for all integers x

Source: Austrian - Polish 1994 APMC

May 3, 2020
number theorydividesdivisible

Problem Statement

Determine all two-digit positive integers n=ab‾n =\overline{ab} (in the decimal system) with the property that for all integers xx the difference xa−xbx^a - x^b is divisible by nn.
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