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Some special equations in a finite field

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References

  1. N. C. Ankeny, Equations in finite fields, Proc. Nat. Acad. Sci. USA. 40 (1954), 1072–1073.

    Google Scholar 

  2. F. A. Behrend, Generalization of an inequality of Heilbronn and Rohrbach, Bull. Amer. Math. Soc. 54 (1948), 681–684.

    Google Scholar 

  3. L. Carlitz, Invariantive theory of equations in a finite field, Trans. Amer. Math. Soc. 75 (1953), 405–427.

    Google Scholar 

  4. L. Carlitz, The number of solutions of certain types of equations in a finite field, Pac. J. Math., vol. 5 (1955), 177–181.

    Google Scholar 

  5. L. Carlitz, The number of solutions of a particular equation in a finite field. Publicationes Mathematicae, to appear.

  6. L. Carlitz andH. H. Corson, Some special equations in a finite field, Proc. Nat. Acad. Sci USA., vol. 41 (1955), 752–754.

    Google Scholar 

  7. H. Davenport andH. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. reine angew.Math. 172 (1935), 151–182.

    Google Scholar 

  8. O. B. Faircloth, On the number of solutions of some general types of equations in a finite field, Can. J. Math. 4 (1952), 343–351.

    Google Scholar 

  9. H. A. Heilbronn, On an inequality in the elementary theory of numbers, Proc. Camb. Phil. soc. 33 (1937), 207–209.

    Google Scholar 

  10. L. K. Hua andH. S. Vandiver, On the existence of solutions of certain equations in a finite field, Proc Nat. Acad. Sci. USA. 34 (1948), 258–263.

    Google Scholar 

  11. L. K. Hua andH. S. Vandiver, On the nature of solutions of certain equations in a finite field, Proc. Nat. Acad. Sci. USA. 35 (1949), 481–487.

    Google Scholar 

  12. L. K. Hua andH. S. Vandiver, On the number of solutions of some trinomial equations in a finite field, Proc. Nat. Acad. Sci. USA. 35 (1949), 477–481.

    Google Scholar 

  13. H. Rohrbach, Beweis einer zahlentheoretischen Ungleichung, J. reine angew. Math. 177 (1937), 193–196.

    Google Scholar 

  14. St. Schwarz, On Waring's problem for finite fields, Quart. J. of Math. (Oxford) 19 (1948), 123–128.

    Google Scholar 

  15. A. Weil, Number of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497–508.

    Google Scholar 

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  1. Durham, N. C., USA

    L. Carlitz & H. H. Corson

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  1. L. Carlitz
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  2. H. H. Corson
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Carlitz, L., Corson, H.H. Some special equations in a finite field. Monatshefte für Mathematik 60, 114–122 (1956). https://doi.org/10.1007/BF01300456

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