Question: (2) Consider the following problems in modular arithmetic. Justify every step in your solution. (a) Evaluate the modular powers 219222 (mod 348) and 393'7'35'1'ri'2 (mod

(2) Consider the following problems in modular arithmetic. Justify every step in your solution. (a) Evaluate the modular powers 219222 (mod 348) and 39\"\"3'7'35'1'ri'2 (mod 11) (5+5 marks). (b) Solve each of the following modular equations for :r: (i) 1254523: 4 E 4 (mod 15044) (5 marks), (ii) 37:1: 2 E 1 (mod 94) (5 marks). The order of operations for modular arithmetic is the same as that of ordinary arithmetic; that is, the multiplication goes before addition. (c) Verify the answer of each modular power and each equation in sagemath. This means writing sagemath code to answer each question (1+1+1+1 marks). (11 1

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