2014/020) If 3^n+81 is a perfect square, find a positive integer value of n.

3^n+ 81 = m^2=>3^n = m^2-81 = (m+9)(m-9)

So we need to find 2 powers of 3(not necessarily consecutive so that difference is 18) we have 1,3,9,27,81 giving 9 and 27.

So n = 5 and m = 18