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122^n - 102^n - 21^n is one less than a multiple of 2020

Source: New Zealand MO 2019 Round 1 p4

September 20, 2021
number theorydividesdivisiblemultiple

Problem Statement

Show that the number 122n−102n−21n122^n - 102^n - 21^n is always one less than a multiple of 20202020, for any positive integer nn.
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