Product representations of polynomials over finite fields
Acta Arithmetica
MSC: Primary 11B30; Secondary 11T06, 05D05
DOI: 10.4064/aa260123-9-8
Published online: 22 September 2026
Abstract
Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of $\{1,\ldots , N\}$ 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.
