Abstract:Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of $\{1,2,\ldots, N\}$ such that it does not contain $k$ distinct elements whose product is a perfect square. More generally, Verstraëte proposed a conjecture regarding the asymptotic behavior of the same quantity with the set of perfect squares replaced by the value set of a polynomial in $\mathbb{Z}[x]$. In this paper, we study a finite field analogue of Verstraëte's conjecture.
From: Semin Yoo [view email]
[v1]
Fri, 23 Jan 2026 11:20:34 UTC (13 KB)
[v2]
Sun, 9 Aug 2026 09:25:51 UTC (14 KB)
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