Question 3 20 marks You should be able to answer this question after studying Unit 3. (a) (i) Use Euclid's algorithm to nd a multiplicative inverse of 17 module 90, and hence solve the linear congruence 173: E 9 (mod 90). (ii) Explain why the following linear congruence has no solutions: 9:1: E 12 (mod 90). (iii) Solve the linear congruence 273: E 72 (mod 90). (b) The afne cipher E is given by [3(a) E 7:}: + 12 (mod 26). The conversion table for letters and numbers is shown below. (i) Show that 15 is a multiplicative inverse of 7 module 26. (ii) Suppose that you receive the enciphered message 8, 16, 25, 2. Decipher the message and deduce the word that was sent