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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 points)

Deadline expired on 12 October 2015.

Statistics on problem A. 647.
 10 students sent a solution. 5 points: Baran Zsuzsanna, Gáspár Attila, Imolay András, Szabó 789 Barnabás, Williams Kada. 1 point: 3 students. 0 point: 2 students.

• Problems in Mathematics of KöMaL, September 2015

•  Támogatóink: Morgan Stanley