Find all n satisfying divisibility for all elements a of A
Source: Serbia NMO 2010 problem 3
March 11, 2011
number theory unsolvednumber theory
Problem Statement
Let be an infinite set of positive integers. Find all natural numbers such that for each ,
a^n + a^{n-1} + \cdots + a^1 + 1 \mid a^{n!} + a^{(n-1)!} + \cdots + a^{1!} + 1.Proposed by Milos Milosavljevic