**Quadratic Residues and Primitive Roots**

Kevin McGown

Chico State University

Chico, CA

Friday, May 3rd, 4:30 PM Kalkin 001

**AbstractÂ **

Quadratic residues and primitive roots are of fundamental importance in elementary number theory and have applications to factorization algorithms, graph theory, cryptography, and even acoustic engineering. We will begin by introducing the necessary definitions and giving some concrete examples. Then we will discuss the distribution of quadratic residues; character sums will appear naturally in this context. Next we will turn to studying the distribution of primitive roots, and focus on the problem of giving an upper bound on the least primitive root modulo p. In the final part, I will discuss a conjecture of Grosswald and indicate some results of TreviÃ±o, Trudgian, and myself. Most of this talk will be expository in nature and aimed at a general audience. No number theoretic background is required.

ADA: Individuals requiring accommodations, please contact Doreen Taylor at (802) 656-3166