# : 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.

: 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
for x, y e Z. We say that a and b are relatively prime iff gcd(a, b) = 1.
Prove:
Va e Z, Vb e Z, Vc e Z, ac =n bc ^ gcd(c,n) = 1 → a =n b.

(550 words)

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