Cryptography question: answer completely and carefully with full working out for a thumbs up.

Exercise 4: a) Eve has a cryptotext encrypted with an affine cipher E(x) = ax + b (mod 26) from an English-language plaintext. The most frequent cryptotext letter has numerical value a and the second most frequent letter has numerical value B. Show that it is likely that a = 73 7a and b = 3a 28. b) Prove that the affine cipher E(x) = ax + b (mod m) is idempotent. Exercise 4: a) Eve has a cryptotext encrypted with an affine cipher E(x) = ax + b (mod 26) from an English-language plaintext. The most frequent cryptotext letter has numerical value a and the second most frequent letter has numerical value B. Show that it is likely that a = 73 7a and b = 3a 28. b) Prove that the affine cipher E(x) = ax + b (mod m) is idempotent