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.


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

Problems in Mathematics of KöMaL, April 2016