MA-410, Spring 2025, Homework 4, due as indicated for each problem.

All solutions must be submitted on the Moodle web site for the class at wolfware.ncsu.edu. You may upload a photo of your handwritten solution or a file of your typed solution. Note my office hours on my schedule.

  1. Due Thursday, April 17, 11:59pm.
    Using the Tonelli-Shanks Algorithm discussed in class find a residue b modulo 233 such that b2 ≡ 167 (mod 233). For the quadratic non-residue, please use 5 ∈ ℤ233. Please use Maple / wolframalpha.com and show which modular powers r &^ e mod 233 / PowerMod[r,e,233] and modular products you have computed.
  2. Due Tuesday, April 22, 11:59pm.
    ENT, §12.1, Problem 2, page 251: If x, y, z is a primitive Pythagorean triple, prove that x + y is congruent modulo 8 to either 1 or 7, and x – y is congruent modulo 8 to either 1 or 7.