MA-410 Homework 4

Due at 4:59pm in my mailbox in SAS 3151, Wednesday, April 28, 2010


Solutions may only be submitted as paper documents. Note my office hours on my schedule.

  1. Using the algorithm discussed in class, find a residues b0, b1, b2 modulo 5 such that for b = b0 + 5 * b1 + 25 * b2 one has b2 congruent 94 modulo 125.
  2. ENT, §9.3, Problem 1(c), page 190. Please use Eisenstein's method.
  3. ENT, §12.1, Problem 7, page 251.
  4. ENT, §12.2, Problem 9, page 260. Hint: a difficulty is that 2 may divide x but not y, and then the Pythagorean triple (2y2, z, x2) is not easily made primitive. Handle this case separately by considering the equation modulo 16.