Sums of triangular numbers

03/09/2010 - 12:15pm
03/09/2010 - 1:10pm
Wai Kiu Chan (Wesleyan University)

In 1796 Gauss wrote in his mathematical diary the theorem that every natural number is the sum of three triangular numbers. In today's terminology, we say that the sum of three triangular numbers is universal. Later Liouville proved a generalization of Gauss' theorem which determines all ternary sums of triangular numbers that are universal. In this talk, I will describe the recent result by W. Bosma and B. Kane which provides a simple characterization of universal sums of triangular numbers and my joint work with B.K. Oh on almost universal sums of triangular numbers.

Millikan 208 (Pomona College)