Show that there are no positive integers n for which n4 + 2n3 + 2n2 + 2n + 1 is a perfect square. Are there any positive integers n for which n4 +n3 +n2 +n+1 is a perfect square?

Question

Show that there are no positive integers n for which n4 + 2n3 + 2n2 + 2n + 1 is a perfect square. Are there any positive integers n for which n4 +n3 +n2 +n+1 is a perfect square?
If so, find all such n.