Problem B. 4645. (September 2014)
B. 4645. Let \(\displaystyle H_{1}=\{1, 3, 5, \ldots, 2n1\}\) and \(\displaystyle H_{2}=\{1+k, 3+k, 5+k, \ldots, 2n1+k\}\), 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 10 October 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. 
