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A cool sum

Source: Mexico Regional Contest 2012-Problem 5

September 13, 2015
fermat's little theoremnumber theory

Problem Statement

Consider and odd prime pp. For each ii at {1,2,...,p−1}\{1, 2,..., p-1\}, let rir_i be the rest of ipi^p when it is divided by p2p^2. Find the sum: r1+r2+...+rp−1r_1 + r_2 + ... + r_{p-1}
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