(a) (i) Use Euclid's algorithm to find a multiplicative inverse of 23 modulo 75, and hence solve the linear congruence 23x = 19 (mod 75). (ii) Explain why the following linear congruence has no solutions: 25x = 30 (mod 75). (iii) Solve the linear congruence 45x = 60 (mod 75).

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