Show that there are no positive integers n for which [math]n^4 + 2n^3 + 2n^2 + 2n + 1[/math] is a perfect square. Are there any positive integers n for which [math]n^4 + n^3 + n^2 + n + 1[/math] is a perfect square? If so, how do you find all such n?
Are there any positive integers [math]n[/math] for which [math]n^4 + n^3 + n^2 + n + 1[/math] is a perfect square?