Geodesic
On the number of points on one class of curves in a ring of residues
Problemy fiziki, matematiki i tehniki, no. 4 (2020), pp. 98-104

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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
Mots-clés : indices modulo $2^\alpha$. 
@article{PFMT_2020_4_a17,
     author = {V. I. Murashka and A. A. Piachonkin},
     title = {On the number of points on one class of curves in a ring of residues},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {98--104},
     publisher = {mathdoc},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_4_a17/}
}
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V. I. Murashka; A. A. Piachonkin. On the number of points on one class of curves in a ring of residues. Problemy fiziki, matematiki i tehniki, no. 4 (2020), pp. 98-104. http://geodesic.mathdoc.fr/item/PFMT_2020_4_a17/