The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that divides both a and b. One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax + by or x, y e Z. We say that a and b are relatively prime iff gcd(a, b) = 1. %3D Prove: Va e Z, Vb e Z, Vc e Z, ac =, bc ^ gcd(c,n) = 1 → a =n b.

Question
The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that divides both a and b.
One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax + by
or x, y e Z. We say that a and b are relatively prime iff gcd(a, b) = 1.
%3D
Prove:
Va e Z, Vb e Z, Vc e Z, ac =, bc ^ gcd(c,n) = 1 → a =n b.
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Transcribed Image Text

The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that divides both a and b. One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax + by or x, y e Z. We say that a and b are relatively prime iff gcd(a, b) = 1. %3D Prove: Va e Z, Vb e Z, Vc e Z, ac =, bc ^ gcd(c,n) = 1 → a =n b.

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