Math 504--Summer 2002

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  w23 = 1 and
w22 + w21 + w20 + ... + w2 + 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.