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Proceedings of the American Mathematical Society

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Note on Brewer's character sum


Author: Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 71 (1978), 153-154
MSC: Primary 10G05
MathSciNet review: 0472725
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Abstract: A very short proof is given of the result

$\displaystyle \sum\limits_{x = 0}^{p - 1} {\left( {\frac{{(x + 2)({x^2} - 2)}}{p}} \right)} = 0,$

if $ p \equiv 5$ or $ 7 \pmod 8$.

References [Enhancements On Off] (What's this?)

  • [1] B. W. Brewer, On certain character sums, Trans. Amer. Math. Soc. 99 (1961), 241-245. MR 0120202 (22:10959)
  • [2] P. A. Leonard and K. S. Williams, Jacobi sums and a theorem of Brewer, Rocky Mountain J. Math. 5 (1975), 301-308; erratum, ibid. 6 (1976), 509. MR 0366831 (51:3077)
  • [3] A. R. Rajwade, Certain classical congruences via elliptic curves, J. London Math. Soc. 8 (1974), 60-62. MR 0338001 (49:2768)
  • [4] A. L. Whiteman, A theorem of Brewer on character sums, Duke Math. J. 30 (1963), 545-552. MR 0154857 (27:4801)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0472725-1
Article copyright: © Copyright 1978 American Mathematical Society