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7^{2n} -48^n - 1 is always divisible by 9

Source: Greece JBMO TST 2017, Problem 3

June 25, 2018
number theoryDivisibility

Problem Statement

Prove that for every positive integer nn, the number An=72n−48n−1A_n = 7^{2n} -48n - 1 is a multiple of 99.
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