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Mathematics of the USSR-Izvestiya, 1972, Volume 6, Issue 4, Pages 677–704
DOI: https://doi.org/10.1070/IM1972v006n04ABEH001895 (Mi im2329) 		 
Congruences in two unknowns

S. A. Stepanov
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DOI: https://doi.org/10.1070/IM1972v006n04ABEH001895
Abstract: The paper investigates the number $I_p$ of solutions of an algebraic congruence $F(x,y)\equiv0\pmod p$, where $p$ is a prime. Under certain conditions for the polynomial $F(x,y)$ the asymptotic formula $I_p=p+O(p^{1/2})$ is obtained by elementary methods.
Received: 16.11.1971
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1972, Volume 36, Issue 4, Pages 683–711
Bibliographic databases:
UDC: 511
MSC: Primary 10A10; Secondary 12A05
Language: English
Original paper language: Russian
Citation: S. A. Stepanov, “Congruences in two unknowns”, Izv. Akad. Nauk SSSR Ser. Mat., 36:4 (1972), 683–711; Math. USSR-Izv., 6:4 (1972), 677–704
Citation in format AMSBIB
\Bibitem{Ste72}
\by S.~A.~Stepanov
\paper Congruences in two unknowns
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 4
\pages 683--711
\mathnet{http://mi.mathnet.ru/im2329}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=314848}
\zmath{https://zbmath.org/?q=an:0241.10002}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 4
\pages 677--704
\crossref{https://doi.org/10.1070/IM1972v006n04ABEH001895}
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:262
    English version PDF:5
    References:54
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