Prove that there are infinitely many primes p such that p = 1 (mod 4). Hint: Suppose that there are only finitely many such primes P₁, P₂, ..., Pₖ and consider the integer A= (2P₁P₂ ..Pₖ)² +1 Explain why no prime factor q of A can be equal to Pj, j = 1, 2, ..., k, and why every such factor q must have the property q = 1(mod 4).