New congruences modulo 5 and 9 for partitions with odd parts distinct

被引：9

作者：

Fang, Houqing ^{[1
]}

Xue, Fanggang ^{[1
]}

Yao, Olivia X. M. ^{[1
]}

机构：

[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China

来源：

QUAESTIONES MATHEMATICAE | 2020年 / 43卷 / 11期

基金：

美国国家科学基金会;

关键词：

Congruence; partition; odd parts distinct; theta function; sum of triangular numbers; CONJECTURES; SQUARES; NUMBER; SUMS; SUN;

D O I：

10.2989/16073606.2019.1653394

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established. In this paper, we establish the generating function of pod(5n + 2) and then prove new infinite families of congruences modulo 5 and 9 for pod(n) by using the formulas for t(3)(n) and t(5)(n), where t(k) (n) is the number of representations of n as a sum of k triangular numbers. In particular, we generalize a congruence for pod(n) due to Radu and Sellers.

引用

页码：1573 / 1586

页数：14

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