Author

Hong-Bin Zhao

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Preprint Sep 2026

Equal subset sums and close divisors

For $k\geq2$, let $\alpha_k$ be the supremum of the exponents $a$ for which almost every integer $n$ has $k$ distinct divisors in a multiplicative interval of relative length $(\log n)^{-a}$. Select each positive integer $i$ independently with probability $1/i$, forming a random set $\mathbf A$, and let $\beta_k$ be th...

Jian-Feng Hou, Hong-Bin Zhao · 0 citations

Preprint Sep 2026

Asymptotically optimal packings of arithmetic progressions with prime differences

For a positive integer $n$, put $A_d=\{id:1\le i\le\lfloor n/d\rfloor\}$ for $1\le d\le n$ and $B_d=\{id:1\le i\le n\}$ for $d\in\mathbb{N}$. For $D\subseteq\{1,\ldots,n\}$, let $m_D(n)$ be the minimum length of an integer interval containing pairwise disjoint shifted copies of $A_d$ for all $d\in D$. For a finite set...

Jian-Feng Hou, Si-Yue Liu, Hong-Bin Zhao · 0 citations