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

Use Euclid’s algorithm to find integers x, y and d for which 3936 x + 1293 y = d is the smallest possible positive integer. Using your answers to this as your starting point, do the following tasks. (a) Find a solution of 3936 x ≡ d mod 1293. (b) Find an integer r that has the property that r ≡ d mod 1293 and r ≡ 0 mod 3936. (c) Find an integer R that has the property that R ≡ 126 mod 1293 and R ≡ 0 mod 3936. (d) Find an integer s that has the property that s ≡ d mod 3936 and s ≡ 0 mod 1293. (e) Find an integer S that has the property that S ≡ 573 mod 3936 and S ≡ 0 mod 1293. (f) Find an integer T that has the property that T ≡ 126 mod 1293 and T ≡ 573 mod 3936. (g) Is T the only number satisfying those two congruences; if not, which other numbers?

Expert Solution

Colby Messinger answered 2 years ago

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...

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