Finding equation has no solutions mod m

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Reference no: EM1347607

Q1) (a) Let the equation ax = b mod m, where x is unknown and a, b and m are given. Illustrate that this equation has either no solutions mod m, or d solutions mod m, where d = gcd(a, m); also, describe when each of these two cases holds. Consider (non-modular) integer equation ax - km = b (for some integer k), and consider dividing by d.

(b) Using your answer from the previous part, describe all the solutions mod 63 of each of the following three equations:

(i) 4x + 28 = 2 mod 63
(ii) 7x + 50 = 35 mod 63
(iii) 7x + 50 = 36 mod 6

Reference no: EM1347607

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