Numbers and Sets | Part IA, 2004

(a) Use Euclid's algorithm to find positive integers m,nm, n such that 79m100n=179 m-100 n=1.

(b) Determine all integer solutions of the congruence

237x21(mod300)237 x \equiv 21(\bmod 300)

(c) Find the set of all integers xx satisfying the simultaneous congruences

x8(mod79)x11(mod100)\begin{aligned} &x \equiv 8(\bmod 79) \\ &x \equiv 11(\bmod 100) \end{aligned}

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