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Tasty Number Theory

Source: Swiss Final Round 2020 First Exam Problem 4

March 1, 2020
number theoryEulertotient functionfunction

Problem Statement

Let φ\varphi denote the Euler phi-function. Prove that for every positive integer nn
2n(n+1)∣32⋅φ(22n−1).2^{n(n+1)} | 32 \cdot \varphi \left( 2^{2^n} - 1 \right).
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