Tsz Ho Chan

activity

20132025

collaborators

6 papers

math.NT2025

Numbers with Four Close Factorizations

Tsz Ho Chan, Laura Holmes, Michael Liu +1

In this paper, we study numbers $n$ that can be factored in four different ways as $n = A B = (A + a_{1}) (B - b_{1}) = (A + a_{2}) (B - b_{2}) = (A + a_{3}) (B - b_{3})$ with $B \leq A$ , $1 \l…

math.NT2025

A note on three consecutive powerful numbers

Tsz Ho Chan

This note concerns the non-existence of three consecutive powerful numbers. We use Pell equations, elliptic curves, and second-order recurrences to show that there are no such trip…

math.NT2021

New small gaps between squarefree numbers

Tsz Ho Chan

In this paper, we show that, for some constant $C > 0$ , the interval $(x, x + C x^{5/26}]$ always contains a squarefree number when $x$ is sufficiently large (in terms of $C$ ). Our…

math.NT2015

Shortest Distance in Modular Cubic Polynomials

Tsz Ho Chan

In this paper, we study how small a box contains at least two points from a modular cubic polynomial $y \equiv a x^{3} + b x^{2} + c x + d (mod p)$ with $(a, p) = 1$ . We prove that som…

math.NT2015

Shortest Distance in Modular Hyperbola and Least Quadratic Nonresidue

Tsz Ho Chan

In this paper, we study how small a box contains at least two points from a modular hyperbola $x y \equiv c (mod p)$ . There are two such points in a square of side length $p^{1/4 +…

math.NT2013

Numbers with three close factorizations

Tsz Ho Chan

In this paper, we study numbers $n$ that can be factored in three different ways as $n = A_{1} B_{1} = A_{2} B_{2} = A_{3} B_{3}$ where $A_{1}$ , $A_{2}$ , $A_{3}$ are close to each other and $B_{1}$ , $…