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Pitchayut Saengrungkongka

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Preprint Sep 2026

Sparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture

A subset $A\subseteq \mathbb N_0$ is $k$-AP covering if there exists a constant $n_0$ such that for every integer $x>n_0$, there exists $d\in\mathbb N_0$ such that $x-d, x-2d,\dots,x-(k-1)d$ are all in $A$. Disproving a conjecture of Kiss, S\'andor, and Yang, we prove that for every integer $k\geq 6$, there exists a co...

Pitchayut Saengrungkongka · 0 citations