SOLVED: 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 ∈ Z. We say that a and b are relatively prime if gcd(a, b) = 1. Prove that a and n are relatively prime if and only if there exists an integer s such that sa ≡ 1 (mod n). We call s the inverse of a modulo n.

1.1 Compute the greatest common divisor gcd(455, 1235) by hand.

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