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Prove or disprove the following statements. a) ∀a, b ∈ N, if ∃x, y ∈ Z...

Prove or disprove the following statements.

a) ∀a, b ∈ N, if ∃x, y ∈ Z and ∃k ∈ N such that ax + by = k, then gcd(a, b) = k

b) ∀a, b ∈ Z, if 3 | (a 2 + b 2 ), then 3 | a and 3 | b.

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