Mehdi Makhul

activity

20182021

collaborators

9 papers

math.CO2021

On sets of points in general position that lie on a cubic curve in the plane and determine lines that can be pierced by few points

Mehdi Makhul, Rom Pinchasi

Let $P$ be a set of $n$ points in general position in the plane. Let $R$ be a set of points disjoint from $P$ such that for every $x, y \in P$ the line through $x$ and $y$ contains…

math.NT2021

Normality of the Thue-Morse function for finite fields along polynomial values

Mehdi Makhul, Arne Winterhof

Let $F_{q}$ be the finite field of $q$ elements, where $q = p^{r}$ is a power of the prime $p$ , and $(β_{1}, β_{2}, \dots, β_{r})$ be an ordered basis of $F_{q}$ …

math.CO2020

The Elekes-Szabó Problem and the Uniformity Conjecture

Mehdi Makhul, Oliver Roche-Newton, Sophie Stevens +1

In this paper we give a conditional improvement to the Elekes-Szabó problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}…

math.NT2020

No perfect triangle is isosceles

Mehdi Makhul

A perfect triangle is a triangle with rational sides, medians, and area. In this article, we use a similar strategy due to Pocklington to show that if $Δ$ is a perfect triangle, th…

math.CO2020

The Spherical Kakeya Problem in Finite Fields

Mehdi Makhul, Audie Warren, Arne Winterhof

We study subsets of the $n$ -dimensional vector space over the finite field $F_{q}$ , for odd $q$ , which contain either a sphere for each radius or a sphere for each first coo…

math.CO2019

On the number of perfect triangles with a fixed angle

Mehdi Makhul

Richard Guy asked the following question: can we find a triangle with rational sides, medians, and area? Such a triangle is called a \emph{perfect triangle} and no example has been…