Question: 1. Before proceeding, review the formal definition of congruence modulo n.
(a) Prove (directly) that if a ≡ b (mod n) and c ≡ d (mod n), then ac ≡ bd (mod n).
(b) Prove that if a ≡ b (mod n), then ak ≡ bk (mod n).
(c) Is 9257 ≡ 657 (mod 43)? Explain.
2. Describe three different algorithms you use in everyday life. Write them as lists of instructions in human-readable form. What changes would need to be made for these instructions to be specific enough for a machine to follow?