Review Questions, due Sept 30

Which topics and theorems do you think are the most important out of those we have studied?

Division Algorithm, Euclidean Algorithm, Fundamental Thrm of Arithmetic, GCD and LMC, Congruences, Fermat's Thrm, Euler phi function, solving polynomial congruences, Chinese Remainder Thrm, quadratic residue, legrendre and jacobi symbols,

What kinds of questions do you expect to see on the exam?

I expect to see some proof of some thrms, also some computation like solving a polynomial congruence. I also expect to see a problem on quadratic residues, maybe also a question using GCD's or LMC's.

What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Friday.

I need to work on understanding proofs involving quadratic residues better.
Show that if p is congruent to 1 (mod 3), then (−3/p) = 1.