Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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 October 12, 2015.

### Statistics:

 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