IMO 2009 Shortlist N6

Let k be a positive integer. Show that if there exists a sequence a0,a1,... of integers satisfying the condition an = an...

imomathematicsolympiadshortlistnumber-theory

IMO 2009 Shortlist N6

Category: Number Theory

Problem

Let k be a positive integer. Show that if there exists a sequence a0,a1,... of integers satisfying the condition an = an−1 + nk n for all n ≥ 1, then k − 2 is divisible by 3.