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A. 628. Is it true that for every infinite sequence $\displaystyle x_1,x_2,\ldots$ of integers satisfying $\displaystyle |x_{k+1}-x_k|=1$ for every positive integer $\displaystyle k$, there exists a sequence $\displaystyle k_1<k_2<\ldots<k_{2014}$ of positive integers such that as well the indices $\displaystyle k_1,k_2,\ldots,k_{2014}$ as the numbers $\displaystyle x_{k_1},x_{k_2},\ldots,x_{k_{2014}}$ (in this order) form arithmethic progressions?

Proposed by: E. Csóka, Warwick and Ben Green, Oxford

(5 points)

Deadline expired on 10 December 2014.

Statistics on problem A. 628.
 2 students sent a solution. 0 point: 2 students.

• Problems in Mathematics of KöMaL, November 2014

•  Támogatóink: Morgan Stanley