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digits

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March 5, 2005
AMCAIMEUSA(J)MOUSAMOmodular arithmeticLaTeXbinomial coefficients

Problem Statement

Prove that for all a∈{0,1,2,…,9}a\in\{0,1,2,\ldots,9\} the following sum is divisible by 10: Sa=a‾2005+1a‾2005+2a‾2005+⋯+9a‾2005. S_a = \overline{a}^{2005} + \overline{1a}^{2005} + \overline{2a}^{2005} + \cdots + \overline{9a}^{2005}.
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