Someone observed in class that, with an affine cipher (for the alphabet used in Eng- lish, with 26 letters), two letters are always sent to themselves.

(a) This is in fact true. Explain why. (Hint: Solve the equation that says a letter is sent to itself, keeping in mind that multiplication is always done with an odd number not equal to 13.)

(b) Suppose you know the two letters sent to themselves. Is that enough information to tell what the affine cipher is? Explain why or why not.