Geodesic
Congruences in two unknowns
Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 677-704

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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. 
@article{IM2_1972_6_4_a0,
     author = {S. A. Stepanov},
     title = {Congruences in two unknowns},
     journal = {Izvestiya. Mathematics },
     pages = {677--704},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a0/}
}
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S. A. Stepanov. Congruences in two unknowns. Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 677-704. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a0/