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JOURNALS // Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics) // Archive

PFMT, 2020 Issue 4(45), Pages 98–104 (Mi pfmt753)

MATHEMATICS

On the number of points on one class of curves in a ring of residues

V. I. Murashkaa, A. A. Piachonkinb

a F. Scorina Gomel State University
b Moscow Institute of Physics and Technology

Abstract: The number of points on a curve $x^m\equiv y^k\pmod n$ is calculated. The concept of $m/k$-power residue (rational power residue) is introduced. Let n be a natural number. The number of rational power residues modulo n is calculated. As a corollary the classic result on the number of quadratic residues is obtained.

Keywords: algebraic curve, number of points on an algebraic curve, power residue, primitive root, indices modulo $2^\alpha$.

UDC: 511.2

Received: 21.06.2020



© Steklov Math. Inst. of RAS, 2025