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

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Advance Math

Use Euclid’s algorithm to find integers x, y and d for which3936 x + 1293 y = d is the smallest possible positive integer.Using your answers to this as your starting point, do the followingtasks. (a) Find a solution of 3936 x ? d mod 1293. (b) Find aninteger r that has the property that r ? d mod 1293 and r ? 0 mod3936. (c) Find an integer R that has the property that R ? 126 mod1293 and R ? 0 mod 3936. (d) Find an integer s that has theproperty that s ? d mod 3936 and s ? 0 mod 1293. (e) Find aninteger S that has the property that S ? 573 mod 3936 and S ? 0 mod1293. (f) Find an integer T that has the property that T ? 126 mod1293 and T ? 573 mod 3936. (g) Is T the only number satisfyingthose two congruences; if not, which other numbers?

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