Qingqing Zheng

collaborators

6 papers

math.NT2023

New congruences for 4,6-regular partitions modulo primes

Qi-Yang Zheng

The main result of the paper is the existence of an infinitely many families of Ramanujan-type congruences for $b_{4} (n)$ and $b_{6} (n)$ modulo primes $m \geq 2$ and $m \geq 5$ , respec…

math.NT2023

Fibonacci-like property of partition function

Qi-Yang Zheng

The main result of the paper is the Fibonacci-like property of the partition function. The partition function $p (n)$ has a property: $p (n) \leq p (n - 1) + p (n - 2)$ . Our result shows t…

math.NT2022

Repeated values of some restricted divisor functions

Qi-Yang Zheng

We prove that $d_{k} (n) = d_{k} (n + B)$ infinitely often for any positive integers $k$ and $B$ , where $d_{k} (n)$ denotes the number of divisors of $n$ coprime to $k$ .

math.NT2022

There are infinitely many (-1,1)-Carmichael numbers

Qi-Yang Zheng

We prove that there exist infinitely many (-1,1)-Carmichael numbers, that is, square-free, composite integers n such that p+1 divides n-1 for each prime p dividing n.

math.NT2022

Divisibility and distribution of 5-regular partitions

Qi-Yang Zheng

In this paper we study $b_{5} (n)$ , the $5$ -regular partitions of $n$ . Using the theory of modular forms, we prove several theorems on the divisibility and distribution properties of…

math.NT2022

Distribution of 3-regular and 5-regular partitions

Qi-Yang Zheng

In this paper we study the function $b_{3} (n)$ and $b_{5} (n)$ , which denote the number of $3$ -regular partitions and $5$ -regular partitions of $n$ respectively. Using the theory of mod…