Xiumei Li

activity

20122019

collaborators

4 papers

math.NT2019

A proof of Sondow's conjecture on the Smarandache function

Xiumei Li, Min Sha

The Smarandache function of a positive integer $n$ , denoted by $S (n)$ , is defined to be the smallest positive integer $j$ such that $n$ divides the factorial $j!$ . In this note, we…

math.NT2019

Polynomial analogue of the Smarandache function

Xiumei Li, Min Sha

In the integer case, the Smarandache function of a positive integer $n$ is defined to be the smallest positive integer $k$ such that $n$ divides the factorial $k!$ . In this paper,…

math.NT2018

Congruence preserving functions in the residue class rings of polynomials over finite fields

Xiumei Li, Min Sha

In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting…

math.NT2012

On the Selmer groups and Mordell-Weil groups of elliptic curves $y^{2} = x (x \pm p) (x \pm q)$ over imaginary quadratic number fields of class number one

Xiumei Li

Let $p$ and $q$ be odd prime numbers with $q - p = 2,$ the $φ -$ Selmer groups, Shafarevich-Tate groups ( $φ -$ and $2 -$ part) and their dual ones as well the Mordell-Weil grou…

A proof of Sondow's conjecture on the Smarandache function

Polynomial analogue of the Smarandache function

Congruence preserving functions in the residue class rings of polynomials over finite fields

On the Selmer groups and Mordell-Weil groups of elliptic curves y2=x(x±p)(x±q) over imaginary quadratic number fields of class number one

On the Selmer groups and Mordell-Weil groups of elliptic curves $y^{2} = x (x \pm p) (x \pm q)$ over imaginary quadratic number fields of class number one