PUMaC 2009 · 数论（A 组） · 第 8 题

PUMaC 2009 — Number Theory (Division A) — Problem 8

Find the largest positive integer k such that φ ( σ (2 )) = 2 . ( φ ( n ) denotes the number of positive integers that are smaller than n and relatively prime to n , and σ ( n ) denotes the sum 32 of divisors of n ). As a hint, you are given that 641 | 2 + 1. 1

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