[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180045

THE NUMBER OF REPRESENTATIONS BY A TERNARY SUM OF TRIANGULAR NUMBERS

Kim, Mingyu (Department of Mathematical Sciences Seoul National University)
Oh, Byeong-Kweon (Department of Mathematical Sciences and Research Institute of Mathematics Seoul National University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.1, 2019 , pp. 67-80 More about this Journal

Abstract

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

Keywords

representations of ternary quadratic forms; squares;

Citations & Related Records

Reference

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