Problem A. 647. (September 2015)
A. 647. Let \(\displaystyle k\) be a nonnegative integer. Prove that there are only finitely many positive integers \(\displaystyle n\) for which there exist two disjoint sets \(\displaystyle A\) and \(\displaystyle B\) satisfying \(\displaystyle A \cup B = \{1; 2; \ldots; n\}\) and \(\displaystyle \displaystyle\left\prod \limits_{a \in A} {a}  \prod\limits _{b
\in B} {b}\right=k\).
Proposed by: Balázs Maga, Budapest
(5 pont)
Deadline expired on 12 October 2015.
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