IMO 2007 Shortlist N2

Let b,n > 1 be integers. Suppose that for each k > 1 there exists an integer ak such that b − an k is divisible by k. Pr...

imomathematicsolympiadshortlistnumber-theory

IMO 2007 Shortlist N2

Category: Number Theory

Problem

Let b,n > 1 be integers. Suppose that for each k > 1 there exists an integer ak such that b − an k is divisible by k. Prove that b = An for some integer A. (Canada)