Yulu Feng

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math.NT2021

On the sums of squares of exceptional units in residue class rings

Yulu Feng, Shaofang Hong

Let $n \geq 1, e \geq 1, k \geq 2$ and $c$ be integers. An integer $u$ is called a unit in the ring $Z_{n}$ of residue classes modulo $n$ if $g cd (u, n) = 1$ . A unit $u$ is called a…

math.NT2021

On the number of zeros to the equation $f (x_{1}) + ... + f (x_{n}) = a$ over finite fields

Chaoxi Zhu, Yulu Feng, Shaofang Hong +1

Let $p$ be a prime, $k$ a positive integer and let $F_{q}$ be the finite field of $q = p^{k}$ elements. Let $f (x)$ be a polynomial over $F_{q}$ and $a \in F_{q}$ . We d…

math.NT2018

A generalization of a theorem of Nagell

Yulu Feng, Shaofang Hong, Xiao Jiang +1

Let $n$ be a positive integer. In 1915, Theisinger proved that if $n \geq 2$ , then the $n$ -th harmonic sum $\sum_{k = 1}^{n} \frac{1}{k}$ is not an integer. Let $a$ and $b$ be positive in…

On the sums of squares of exceptional units in residue class rings

On the number of zeros to the equation f(x1​)+...+f(xn​)=a over finite fields

A generalization of a theorem of Nagell

On the number of zeros to the equation $f (x_{1}) + ... + f (x_{n}) = a$ over finite fields