Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 670. (April 2016)

A. 670. Let $\displaystyle a_1,a_2,\ldots$ be a sequence of nonnegative integers such that

$\displaystyle \sum_{i=1}^{2n} a_{id} \le n$

holds for every pair $\displaystyle (n,d)$ of positive integers. Prove that for every positive integer $\displaystyle K$, there are some positive integers $\displaystyle N$ and $\displaystyle D$ such that

$\displaystyle \sum_{i=1}^{2N} a_{iD} = N-K.$

(Chinese problem)

(5 pont)

Deadline expired on May 10, 2016.

Statistics:

 1 student sent a solution. 5 points: Williams Kada.

Problems in Mathematics of KöMaL, April 2016