a=(2n+1) (3n+2)
All we need is one counter-example to prove that this is not a perfect square.....let n = 1....and we have
a = (2(1) + 1) (3(1) + 2) = (3)(5) = 15 and that is not a perfect square....
For this to be a perfect square, both linear factors would have to be the same.....