MA-410 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Thursday, February 28, 2019


All solutions must be submitted stapled in hardcopy either to me in class or placed in my mailbox.
Note my office hours on my schedule.

  1. A Mersenne number is an integer of the form Mp = 2p - 1, where p is a prime number. Please prove that no Mersenne prime number is a divisor of a Mersenne number that is larger than the Mersenne prime.
  2. Let the Fermat numbers be Fn= 22n + 1 for integers n ≥ 0. Please prove that 2Fn-1 ≡ 1 (mod Fn) for all n ≥ 0.
  3. ENT, §4.2, Problem 18, page 68.
  4. ENT, §4.4, Problem 7(a), page 83, using the Chinese remainder algorithm from class, which is based on interpolation by divided differences.
  5. ENT, §5.2, Problem 21, page 93.
  6. ENT, §5.2, Problem 19, page 93.