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