Let 1 ≤ m ∈ Z and let a,b ∈ Z be such that gcd(a,b) =...

Question

Question

Let 1 ≤ m ∈ Z and let a,b ∈ Z be such that gcd(a,b) = m. Prove that gcd(a2,b2) = m2.

Answer 1

Answer #1

Given, ged(a,b) = m where 1CM EZ then mla and mlb (by defn of ged) =) a= mag and b=maz for some relatively prime. Then a²m²a?

Answer 2

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