Prove that, for all primes p and q, {px + qy : x, y ∈ Z} = Z if and only if p is not equal q.
Added by Dylan K.
Step 1
We want to show that for every integer z, there exist integers x and y such that px + qy = z. By the Euclidean algorithm, we know that the greatest common divisor of p and q, gcd(p, q), can be expressed as a linear combination of p and q. Since p and q are Show more…
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