MA-410 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Thursday, March 1, 2018


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. Note that for p = 11, M11 = 2047 is divisible by 23 and 89. Please prove that no other Mersenne number is divisible by 23. [Hint: compute 2^(2*k+1) mod 23 for k=1,2,3,... by Maple.]
  2. Please prove that there are infinitely many composite numbers of the form 251 + 6n, n=0,1,2,...
  3. ENT, §4.2, Problem 15, page 68.
  4. ENT, §4.4, Problem 10, page 83, using the Chinese remainder algorithm (based on Newton interpolation) from class.
  5. ENT, §5.2, Problem 12, page 93.
  6. ENT, §5.2, Problem 19, page 93.