Olympiad problem: Erdos-Selfridge The following problem is a special case of Erdos-Selfridge theorem: http://projecteuclid.org/euclid.ijm/1256050816
Problem: Prove that for any positive integer $n$, the product $(n+1)(n+2)...(n+10)$ is not a perfect square.
It appeared as an olympiad problem, so there is a solution using just olympiad techniques (i.e. "elementary" maths), and it shouldn't be too long either because in an olympiad you only have limited time. However, after trying this for almost a day I still couldn't get anything interesting. I've tried simpler versions but it was no use. I would appreciate any help!
EDIT: I couldn't find a solution anywhere, I tried the AoPS contest section. It's from the 2002 Bosnia Herzegovina Team Selection Test, in case anyone wants to try looking.

the product is equal 2^5 x (odd number) . 5 is not even, thus the product cannot be a square.
Best regards
