Library / /100 of 151

, 2014

Combinatorics Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Is it true that for every infinite sequence $x_1,x_2,\ldots$ of integers satisfying $|x_{k+1}-x_k|=1$ for every positive integer $k$ , there exists a sequence $k_1<k_2<\ldots<k_{2014}$ of positive integers such that as well the indices $k_1,k_2,\ldots,k_{2014}$ as the numbers $x_{k_1},x_{k_2},\ldots,x_{k_{2014}}$ (in this order) form arithmethic progressions?
Proposed by: E. Csóka, Warwick and Ben Green, Oxford
(5 pont)

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: KöMaL, licensed Rights held by KöMaL and the MATFUND Foundation. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.