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arXiv · 2404.09575

Binary quadratic forms with the same value set

Étienne Fouvry·Peter Koymans
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Abstract

Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}^2)$ to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$.

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Étienne Fouvry, Peter Koymans. 2024-04-15. Binary quadratic forms with the same value set. https://arxiv.org/abs/2404.09575

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