IMO 2009 Shortlist A6
Suppose that s1,s2,s3,... is a strictly increasing sequence of positive integers such that the subsequences ss1, ss2, ss...
Category: Algebra
Problem
Suppose that s1,s2,s3,... is a strictly increasing sequence of positive integers such that the subsequences ss1, ss2, ss3, ... and ss1+1, ss2+1, ss3+1, ... are both arithmetic progressions. Prove that s1,s2,s3,... is itself an arithmetic progression.