Calculating mod of the number

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Reference no: EM1322713

a) Consider the equation ax = b mod m, where x refers to the unknown and a, b and m are given. Display that this equation has either no solutions mod m, or d solutions mod m, where d = gcd (a, m); also, explain when each of these two cases holds.

b) Utilizing your answer from previous part, explain all the solutions mod 63 of each of the following given three equations:

i) 4x + 28 = 2 mod 63

ii) 7x + 50 = 35 mod 63

iii) 7x + 50 = 36 mod 6

Reference no: EM1322713

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