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.

The given expression is equivalent to: [(n+1)(n+2)-1]^2 - 1

 

Hint: n*(n+2) = n^2-1

e.g. 5*7 = 35 = 36-1 = 6^2 - 1

Posted by anil on 2004-04-06 19:28:35