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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 points)

Deadline expired on 10 October 2014.

Statistics on problem B. 4645.
 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

•  Támogatóink: Morgan Stanley