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Consider the numbers 130 and 57. (1) Use Euclid’s algorithm to find the gcd(57, 130). (2)...

Consider the numbers 130 and 57.

(1) Use Euclid’s algorithm to find the gcd(57, 130).

(2) Find integers x, y so that 57x + 130y = 1.

(3) Find r ∈ {0, 1, , . . . , 130} so that 57r ≡ 1 (mod 129).

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