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arXiv · 2503.12861

Cubic congruences and binary quadratic forms

Zhi-Hong Sun
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Abstract

Let $p>3$ be a prime, $a_1,a_2,a_3\in\Bbb Z$ and let $N_p(x^3+a_1x^2+a_2x+a_3)$ denote the number of solutions to the congruence $x^3+a_1x^2+a_2x+a_3\equiv 0\pmod p$. In this paper, we give an explicit criterion for $N_p(x^3+a_1x^2+a_2x+a_3)=3$ via binary quadratic forms.

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Zhi-Hong Sun. 2025-03-17. Cubic congruences and binary quadratic forms. https://arxiv.org/abs/2503.12861

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