Homework 5

Due Wednesday, May 2:

  1. Section 4.1 (page 244) #9
  2. Section 4.1 (page 245) # 28
  3. Let a, b, and c be integers, and a \neq 0 . Prove that if a | b and b | c, then a | c.
  4. Compute the following:
    • 13569 mod 3
    • 13569 mod 5
    • 6^{20} mod 11
  5. Convert the following numbers from decimal to binary:
    • 111
    • 127
    • 128

Challenge: (Optional) Let a, b and c be any integers, and n > 1. Show that if a \equiv b (mod n) and b \equiv c (mod n), then a \equiv c  (mod n).