### February 4 3:00pm, BRH 208

Rick Luttmann (Sonoma State)

• Title:
Carmichael Numbers
• Abstract:
Carmichael Numbers are composite counterexamples to the converse of Fermat's "Little Theorem". I will explain and prove the Fermat theorem, then consider its converse and why it's false. There is quite a bit known about Carmichael Numbers. It was only a quarter-century ago that it was determined there are infinitely many.

### March 4 3:00pm, BRH 208

Jay Cummings, Quin Darcy and Morgan Throckmorton (Sacramento State)
Natalie Hobson, Drew Horton, Keith Rhodewalt, and Ry Ulmer-Strack (Sonoma State)

• Title:
Counting Pseudo Progressions
• Abstract:
Arithmetic progressions are sequences of numbers in which each consecutive term differ by the same constant. If we allow for more than one common difference between consecutive terms, then the progression is called a pseudo progression; if we allow up to m common differences, then it is called an $m$-pseudo progression. We will explore how to count the number of pseudo progressions in the set $\{1,2,\dots,n\}$, and discuss the applications of this to future work in Ramsey theory.

### April 22 3:00pm, BRH 208

Morgan Throckmorton (Sacramento State)

• Title:
TBA
• Abstract:
TBA