Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4645. (September 2014)

B. 4645. Let $\displaystyle H_{1}=\{1, 3, 5, \ldots, 2n-1\}$ and $\displaystyle H_{2}=\{1+k, 3+k, 5+k, \ldots, 2n-1+k\}$, where $\displaystyle n$ and $\displaystyle k$ are any positive integers. Is there an appropriate $\displaystyle k$ for every $\displaystyle n$ such that the product of all elements of the set $\displaystyle H_{1}\cup H_{2}$ is a perfect square?

(5 pont)

Deadline expired on October 10, 2014.

### Statistics:

 109 students sent a solution. 5 points: 98 students. 4 points: 4 students. 2 points: 1 student. 1 point: 1 student. 0 point: 5 students.

Problems in Mathematics of KöMaL, September 2014