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