MathDB
Number of a with n|a^n+1

Source: Italian tst 2006 / 5

May 27, 2006
modular arithmeticEulernumber theory unsolvednumber theory

Problem Statement

Let nn be a positive integer, and let AnA_{n} be the the set of all positive integers a≤na\le n such that n∣an+1n|a^{n}+1. a) Find all nn such that An≠∅A_{n}\neq \emptyset b) Find all nn such that ∣An∣|{A_{n}}| is even and non-zero. c) Is there nn such that ∣An∣=130|{A_{n}}| = 130?
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