MA-410, Spring 2023, 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.
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Due Thursday, April 20, 11:59pm.
Using the Tonelli-Shanks Algorithm discussed in class
find a residue b modulo 89
such that b2 ≡
55 (mod 89). For the quadratic non-residue,
use 3 ∈ ℤ89. Please show all your work.
Please use Maple/wolframalpha.com
and show which modular powers and products you have computed.
-
Due Thursday April 20, 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.