Assignment 2--due July 31

Laubenbacher and Pengelly, Chapter
4, Exercises 4.34, 4.38, 4.35, 4.28

Hint for 4.38: [Here the letter
w is used for the 23rd root of unity, because this particular word processor
does not have a lower case omega.] You will probably need to use
the facts that w^{23} = 1 and

w^{22} + w^{21} +
w^{20} + ... + w^{2} + w + 1 = 0.

Hint for 4.35 (2): List all of the numbers u such that N(u) = 1. Then show (2) by contradiction: assume that x is reducible, so that x = uv, but that N(x) = 1.

Terminology for 4.28: A quadratic residue mod 3 is just a perfect square mod 3, and a 7th power residue mod 29 is just a perfect 7th power mod 29.