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Integers and divisibility

Source: 2022 Switzerland IMO TST, Problem 6

August 7, 2022
Integersnumber theoryDivisibility

Problem Statement

Let n≥2n \geq 2 be an integer. Prove that if n2+4n+7nn\frac{n^2+4^n+7^n}{n} is an integer, then it is divisible by 11.
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