Senior Thesis

Department of Mathematics
Harvey Mudd College

Jeremy Rouse

Harvey Mudd College Mathematics 2003

Thesis Title: Combinatorial Proofs of Congruences

Thesis Advisor: Prof. Arthur T. Benjamin
Second Reader: Prof. Naiomi Cameron

Combinatorial Proofs of Congruences

Combinatorial technique can frequently provide satisfying "explanations" of various mathematical phenomena. In this thesis, we seek to explain a number of well-known number-theoretic congruences using combinatorial methods. Many of the results we prove involve the Fibonacci sequence and its generalizations.

Read the full thesis in PDF format.