T. Cai

activity

20072019

most citedSigned q-Analogs of Tornheim's Double Series

20 citations · 37 across the 18 of their papers we have counts for

collaborators

18 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.NT2019

On the divisor problem with congruence conditions

Lirui Jia, Wenguang Zhai, Tianxin Cai

Let $d (n; r_{1}, q_{1}, r_{2}, q_{2})$ be the number of factorization $n = n_{1} n_{2}$ satisfying $n_{i} \equiv r_{i} (mod q_{i})$ ( $i = 1, 2$ ) and $Δ (x; r_{1}, q_{1}, r_{2}, q_{2})$ be the error term of the summ…

math.NT2017

Perfect numbers and Fibonacci primes (III)

Hao Zhong, Tianxin Cai

In this article, we consider the Diophantine equation $σ_{2} (n) - n^{2} = A n + B$ with $A = P^{2} \pm 2$ . For some $B$ , we show that except for finitely many computable solutions in the range $n…

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

Congruent numbers on the right trapezoid

Tianxin Cai, Yong Zhang

We introduce and study a new kind of congruent number problem on the right trapezoid.

math.NT2016★ 1 cited

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

On the divisor problem with congruence conditions

Perfect numbers and Fibonacci primes (III)

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

Congruent numbers on the right trapezoid

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