Proof: Let a, b ? N, and assuem that a, b are relatively prime. Then ab is a sum of 2 squares if and only if both a, b are sums of 2 squares.

hint: ? If a, b are both sums of squares, it is easy to see that ab is a sum of 2 squares - we don't need to use the assumption that a, b are relatively prime.

? The other direction requires a powerful tool - use the unique factorization theorem for Z[i].

(3) Let a, be N, and assuem that a, b are relatively prime. Then ab is a sum of 2 squares if and only if both a, b are sums of 2 squares. . If a, b are both sums of squares, it is easy to see that ab is a sum of 2 squares - we don't need to use the assumption that a, b are relatively prime. . The other direction requires a powerful tool - use the unique factorization theorem for Z