Use Euclid’s algorithm to find integers x, y and d for which 3936x + 1293y =...

Use Euclid’s algorithm to find integers x, y and d for which 3936x + 1293y = d is the smallest possible positive integer. Using your answers to this as your starting point, do the following tasks.

(a)Find an integer s that has the property that s ≡ d mod 3936 and s ≡ 0 mod 1293.

(b) Find an integer S that has the property that S ≡ 573 mod 3936 and S ≡ 0 mod 1293.

(c) Find an integer T that has the property that T ≡ 126 mod 1293 and T ≡ 573 mod 3936.

(d) Is T the only number satisfying those two congruences; if not, which other numbers?

Expert Solution

Here we use Diaphantine Equation. i. e. ax+by=c has solution if GCD (a, b) divides c.

Colby Messinger answered 2 years ago

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