MA-410 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Thursday, March 3, 2016


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. Please prove for all integers n ≥ 3 that are divisible by one or more odd prime numbers that 10n + 1 is a composite integer. That's an integer which in radix 10 has a 1 digit followed by n−1 0's followed by a 1.
  2. Please prove that there are infinitely many composite positive integers that are congruent 1 (modulo 6).
  3. ENT, §4.2, Problem 7, page 68.
  4. ENT, §4.4, Problem 18, page 83, using the Chinese remainder algorithm (based on Newton interpolation) from class. [Hint: separate the cases x ≡ 2 (mod 6) and x ≡ 5 (mod 6).]
  5. ENT, §5.2, Problem 10, (b) only, page 92.
  6. ENT, §5.2, Problem 19, page 93.