Haobo Dai

collaborators

2 papers

math.NT2023

The asymptotic formulae of sums of two smooth squares for divisor function

Nanxiang Wang, Haobo Dai

A natural number $n$ is $y$ -smooth if the greatest prime factor of $n$ does not exceed $y$ . Let $s_{1}$ and $s_{2}$ are $y$ -smooth numbers. We consider sums of smooth squares of th…

math.NT2014

Congruences for the number of partitions and bipartitions with distinct even parts

Haobo Dai

Let $p e d (n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $p e d (n)$ modulo $…