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UKMT Senior Kangaroo, 2025

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Kitty claims that for every positive integer $n$ , the product $(5n + 1)(6n - 1)(n^3 - 2)$ is not divisible by $7$ . What is the smallest three-digit value of $n$ which is a counterexample to Kitty's claim?

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