[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180914

THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER BY TRIANGULAR, SQUARE AND DECAGONAL NUMBERS

Isnaini, Uha (Mathematics & Mathematics Education National Institute of Education Nanyang Technological University)
Melham, Ray (School of Mathematical and Physical Sciences University of Technology)
Toh, Pee Choon (Mathematics & Mathematics Education National Institute of Education Nanyang Technological University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.5, 2019 , pp. 1143-1157 More about this Journal

Abstract

Let $T_aD_b(n)$ and $T_aD^{\prime}_b(n)$ denote respectively the number of representations of a positive integer n by $a(x^2-x)/2+b(4y^2-3y)$ and $a(x^2-x)/2+b(4y^2-y)$ . Similarly, let $S_aD_b(n)$ and $S_aD^{\prime}_b(n)$ denote respectively the number of representations of n by $ax^2+b(4y^2-3y)$ and $ax^2+b(4y^2-y)$ . In this paper, we prove 162 formulas for these functions.

Keywords

representations by binary quadratic forms;

Citations & Related Records

Reference

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