Answer Happy

Please clearly write the proof process of the question,thanks
6. (10 points) Prove that (1) (5 points) Define a real number x to be an integer root if x = m for some m € Z and k € xk Z with k ≥ 0. Prove that if x and y are both integer roots, then so is x · y. = 1 (2) (5 points) Let a, b € Z. Prove that if ax + by = 1 for some x, y € Z, then gcd(a, b)