Assume a, b ∈ Z. Prove that if ax + by = 1 for some x,...

Question

Question

Assume a, b ∈ Z. Prove that if ax + by = 1 for some x, y ∈ Z, then gcd(a, b) = 1.

math Advanced-Math

Answer 1

Answer #1

Let, d- gcd (a,b) . Ther, d 0 aibe 2 Then, a a,d / b2 b,d orRome (arx 4bi)d Nov, axby 2 1 Where This is poggíble PLene Upre

Answer 2

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