Undergraduate seminar

Senior Honors Project Defense

Speaker: Jiayuan Wang
Title: A computational method for solving exponential-polynomial Diophantine equations
Date and Time: Friday, December 19, 12:45-1:45
Place: Monroe 267

Combining number theory with computer programming, we developed a novel computational method for solving Diophantine equations of the form f(m) = k*Q^n with respect to integers m and n, where Q>0 and k>0 are fixed integers and f(m) is a second-degree polynomial. Our method involves solving generalized Pell equations and computing periodic zeros of the solution modulo some powers of Q and employs computer algebra system PARI/GP. We use our method for systematic study of such equations and present many numerical results. As an example, we prove that the only solutions to the equation 2m^2 + 1 = 3^n are (m,n) = (0,0), (+/- 1,1), (+/- 2,2), and (+/-11,5).
(Project advisor: Max Alekseyev)