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5^n + 2 x 3^{n-1} + 1 is multiple of 8

Source: Spanish Mathematical Olympiad 1972 P7

December 5, 2022
number theorymultipledividesdivisible

Problem Statement

Prove that for every positive integer nn, the number An=5n+2⋅3n−1+1A_n = 5^n + 2 \cdot 3^{n-1} + 1 is a multiple of 88.
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