This is a preview of subscription content, log in via an institution to check access.
Literature cited
L. Carlitz, D. J. Lewis, W. H. Mills, and E. G. Straus, “Polynomials over finite fields with minimal value sets,” Matematika,8, No. 2, 121–130 (1961).
L. J. Mordell, “A congruence problem of E. G. Straus,” J. London Math. Soc.,38, No. 149, 108–110 (1963).
B. J. Birch and H. P. F. Swinnerton-Dyer, “Note on a problem of Chowla,” Acta Arithm.,5, No. 4, 417–423 (1959).
K. McCann and K. S. Williams, “On the residues of a cubic polynomial (Mod p),” Can. Math. Bull.,10, No. 1, 29–38 (1967).
K. McCann and K. S. Williams, “The distribution of the residues of a quartic polynomial,” Glasgow Math. J.,8, 67–88 (1967).
L. E. Dickson, “The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group,” Ann. Math.,11, 65–120 (1897).
L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, Dover, New York (1958).
L. Carlitz, “A note on permutations in a finite field,” Proc. Am. Math. Soc.,4, No. 4, 538 (1953).
L. Carlitz and Jo Ann Lutz, “A characterization of permutation polynomials over a finite field,” Am. Math. Mon.,85, No. 9, 746–748 (1978).
L. Carlitz, “On the number of distinct values of a polynomial with coefficients in a finite field,” Proc. Jpn. Acad.,31, No. 3, 119–120 (1955).
S. Uchiyama, “Note on the mean value of V(f),” Proc. Jpn. Acad.,31, No. 4, 199–200 (1955).
S. Uchiyama, “Note on the mean value of V(f). II,” Proc. Jpn. Acad.,31, No. 6, 321–323 (1955).
H. Davenport, D. J. Lewis, and A. Schinzel, “Equations of the form f(x)=g(y),” Q. J. Math. Oxford (2),12, No. 48, 304–312 (1961).
A. Schinzel, “Reducibility of polynomials of the form f(x)−g(y),” Colloq. Math.,18, 213–218 (1967).
L. A. Rubel, A. Schinzel, and H. Tverberg, “On difference polynomials and hereditarily irreducible polynomials,” J. Number Theory,12, No. 2, 230–235 (1980).
A. Weil, “Sur les Courbes Algebriques et les Variétés qui s'en Deduisent,” Publ. Inst. Math. Strasbourg,1041 (1948).
I. M. Vinogradov, Foundations of Number Theory [in Russian], Nauka, Moscow (1981).
N. G. Chebotarev, Theory of Algebraic Functions [in Russian], GITTL, Moscow-Leningrad (1948).
P. Griffiths and J. Harris, Principles of Algebraic Geometry [Russian translation], Vol. 1, Mir, Moscow (1982).
W. Hodge and D. Pedoe, Methods of Algebraic Geometry [Russian translation], Vol. 3, IL, Moscow (1955).
W. Hodge and D. Pedoe, Methods of Algebraic Geometry [Russian translation], Vol. 1, IL, Moscow (1954).
N. Bourbaki, Algebra: Polynomials and Fields. Ordered Groups [Russian translation], Nauka, Moscow (1965).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 38, No. 1, pp. 3–14, July, 1985.
The author thanks V. N. Chubarikov for a discussion of the results of this paper.
Rights and permissions
About this article
Cite this article
Mit'kin, D.A. Polynomials with minimal set of values and the equationf (x) = f (y) in a finite prime field. Mathematical Notes of the Academy of Sciences of the USSR 38, 513–520 (1985). https://doi.org/10.1007/BF01137459
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01137459