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3^n+47 cannot divide 20x5^n-2

Source: Turkey TST 2021 P1 Day 1

May 19, 2021
legendre symbolprime numbersDivisibilitynumber theory

Problem Statement

Let nn be a positive integer. Prove that 20⋅5n−23n+47\frac{20 \cdot 5^n-2}{3^n+47} is not an integer.
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