Let n be the smallest positive integer such that n(n+1)(n+2)(n+3) can be expressed as either a perfect square or a perfect cube (not necessarily both).

Find n, or prove that this is not possible.

n(n+1)(n+2)(n+3) is always 1 less than a square, so it cannot be a square. The cube problem is very hard.

 

Posted by Math Man on 2011-08-22 10:57:10