On Some Properties of Two Simultaneous Polygonal Sequences

Journal of integer sequences

关键词: Mock theta functions;    theta functions;    Gaussian polynomials;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Waterloo * Department of Computer Science

【 摘 要 】

This paper focuses on the properties of integers that are simultaneously representable as both m-gonal and n-gonal numbers. Employing hyperbolic geometry, we ascertain both lower and upper bounds on these numbers when there is a finite set of these integers. We then consider the fundamental class of solutions to a generalized Pell-Diophantine equation that relates to these integers, and derive a fast algorithm that can be used to generate them.

【 授权许可】

Unknown