1. 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 natu- ral 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: VaZ, VbZ, Vc EZ, ac n bc gcd (c, n) = 1 → a=n b.

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