A few problems:

1) Show that for positive integers n, n^4 + 3n^2 + 1 is never a perfect square.

2) Let f(n) = 2n^2 + 14n + 25. We see that f(0) = 25 = 5^2. Find two positive integers n such that f(n) is a perfect square.

3) Find all pairs of positive integers (x,y) such that both x^2 + 3y and y^2 + 3x are perfect squares.