Elliptic curves and the residue-counts of $x^2+bx+c/x$ modulo $p$

For any prime $p > 3$ and rational $p$ -integers $b, c$ with $c (b^{3} - 27 c) \equiv̸ 0 (m o d p)$ let $V_{p} (x^{2} + b x + \frac{c}{x})$ be the residue-counts of $x^{2} + b x + \frac{c}{x}$ modulo $p$ as $x$ runs over $1, 2, \dots, p - 1$ . In this paper, we reveal the connection between $V_{p} (x^{2} + b x + \frac{c}{x})$ and the number of points on certain elliptic curve over the field $F_{p}$ .

Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

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Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

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Elliptic curves and the residue-counts of x2+bx+c/xx2+bx+c/x modulo pp

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Elliptic curves and the residue-counts of x2+bx+c/xx2+bx+c/x modulo pp

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Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

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AI智能校验

Elliptic curves and the residue-counts of $x^{2} + b x + c / x$ modulo $p$

讲解博客

AI智能校验