Question

Answer the following question:

1.

a. Use an affine cipher x 7→ 3x + 1 (mod 26) to encode “Baltimore”.

b. Let a and b be integers. What does it mean to say a divides b? Provide a precise definition and include the proper notation.

c. Let a, b, c, and n be integers with n 6= 0. Suppose that a ≡ b (mod n) and b ≡ c (mod n). Prove that a ≡ c (mod n).

d. Use the Euclidean algorithm to find gcd(39, 65). Find integers a and b so that 39a + 65b = gcd(39, 65). The purpose of this question is to demonstrate your understanding of the algorithm, and you are graded solely on the algorithm. Simply writing down gcd(39, 65) and a and b will get you zero points.

Answer 1