Hao Zhong

activity

20162019

collaborators

4 papers

math.NT2019

A Generalization of A Result of Gauss on Primitive Root

Hao Zhong, Tianxin Cai

A primitive root modulo an integer $n$ is the generator of the multiplicative group of integers modulo $n$ . Gauss proved that for any prime number $p$ greater than $3$ , the sum of…

math.CO2019

Bijections between t-Core Partitions and t-Tuples

Hao Zhong

This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, incl…

math.NT2017

On the number of representations of $n = a + b$ with $ab$ a multiple of a polygonal number

Hao Zhong, Tianxin Cai

In this paper, we study the number of representations of a positive integer $n$ by two positive integers whose product is a multiple of a polygonal number.

math.NT2016

A congruence involving the quotients of Euler and its applications (III)

Hao Zhong, Shane Chern, Tianxin Cai

In this paper, we will present several new congruences involving binomial coefficients under integer moduli, which are the continuation of the previous two work by Cai \textit{et a…

A Generalization of A Result of Gauss on Primitive Root

Bijections between t-Core Partitions and t-Tuples

On the number of representations of n=a+b with ab a multiple of a polygonal number

A congruence involving the quotients of Euler and its applications (III)

On the number of representations of $n = a + b$ with $ab$ a multiple of a polygonal number