Describe three different algorithms you use in everyday

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 a^k ≡ b^k (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?