2 citations · 4 across the 5 of their papers we have counts for
5 papers
Super congruences involving alternating harmonic sums modulo prime powers
Zhongyan Shen, Tianxin Cai
In 2014, Wang and Cai established the following harmonic congruence for any odd prime and positive integer , \begin{equation*} \sum\limits_{i+j+k=p^{r}\atop{i,j,k\in \mathca…
A congruence involving alternating harmonic sums modulo
Zhongyan Shen, Tianxin Cai
In 2014, Wang and Cai established the following harmonic congruence for any odd prime and positive integer , \begin{equation*} \sum\limits_{i+j+k=p^{r}\atop{i,j,k\in \mathca…
Perfect Numbers and Fibonacci Primes (II)
Tianxin Cai, Liuquan Wang, Yong Zhang
In this paper, we study the diophantine equation . We prove that except for finitely many computable solutions, all the solutions to this equation with…
Figurate primes and Hilbert's 8th problem
Tianxin Cai, Yong Zhang, Zhongyan Shen
In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures…
Depth reduction of a class of Witten zeta functions
David M. Bradley, Tianxin Cai, Xia Zhou
We show that if a,b,c,d,f are positive integers such that a+b+c+d+f is even, then the Witten zeta value zeta_{sl(4)}(a,b,c,d,0,f) is expressible in terms of Witten zeta functions w…