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
\(\displaystyle
\sum_{i=1}^{2N} a_{iD} = NK.
\)
(Chinese problem)
(5 pont)
Deadline expired on 10 May 2016.
Statistics:
