IMO 2013 Shortlist C5
Let r be a positive integer, and let a0,a1,... be an infinite sequence of real numbers. Assume that for all nonnegative ...
Category: Combinatorics
Problem
Let r be a positive integer, and let a0,a1,... be an infinite sequence of real numbers.
Assume that for all nonnegative integers m and s there exists a positive integer n P rm1,mrs
such that
am am1 ¨¨¨ ams “ an an1 ¨¨¨ ans.
Prove that the sequence is periodic, i.e. there exists some p ě 1 such that an`p “ an for all n ě 0.
(India) Shortlisted problems 5