MA-410 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Thursday, February 27, 2020

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 consider the decimal repunits (10n -1)/9 for n ≥ 2, which are integers that in decimal representation consist of n consecutive 1 digits. Please prove that if a decimal repunit for n is a prime number (for example n=2,19,23,...), then n must be a prime number.
  2. ENT, §5.2, Problem 15(b), page 93.
  3. ENT, §4.4, Problem 7(b), page 83, using the Chinese remainder algorithm from class, which is based on interpolation by divided differences. For the square, please use 25, for the cube 27, and for the fourth power 16.
  4. ENT, §5.2, Problem 12, page 93. Hint: induction on k.
  5. ENT, §5.2, Problem 15(b), page 93.
  6. ENT, §5.2, Problem 19, page 93.