## 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.

- 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
b
^{2} congruent 94 modulo 125.
- ENT, §9.3, Problem 1(c), page 190. Please use Eisenstein's method.
- ENT, §12.1, Problem 7, page 251.
- ENT, §12.2, Problem 9, page 260.
Hint: a difficulty is that 2 may divide x but not y, and then the Pythagorean triple
(2y
^{2}, z, x^{2}) is not easily
made primitive. Handle this case separately by considering the equation modulo 16.