A pair (x,y) of positive integers is called square if x + y and xy are both perfect squares. For example, pair (5,20) is square since 5 + 20 = 52 and 5 x 20 = 102. Prove that no square pairs exists in which one of its numbers is 3.
Primes p and q are called twin primes, if q = p + 2. Prove that the numbers p^4 + 4 and q^4 + 4 are never relatively prime, if p and q are twin primes.