Congruences for arithmetic functions

被引：0
作者：
Ma, Wu-Xia [1 ,2 ]
Chen, Yong-Gao [1 ,2 ]
机构：
[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China
[2] Nanjing Normal Univ, Inst Math, Nanjing 210023, Peoples R China
来源：
RAMANUJAN JOURNAL | 2022年 / 58卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Arithmetic functions; Congruences; Divisor function; Sum-of-divisors function; Euler's totient function; Colored partitions; VALUES; EULER;
D O I：
10.1007/s11139-021-00454-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Motivated by congruences for partitions, we study congruences for three well known arithmetic functions: the divisor function d(n), the sum-of-divisors function sigma(n) and Euler's totient function phi(n). In this paper, for f(n) = d(n), sigma(n), phi(n) we determine all a, b, c, m such that f(an + b) equivalent to c (mod m) for all nonnegative integers n. These results are useful to find congruences for generalized colored partitions.
引用
收藏
页码：651 / 666
页数：16
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