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Bulletin of the American Mathematical Society

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The number of solutions of a trinomial congruence involving a $k$th power and a square


Author: J. T. Cross
Journal: Bull. Amer. Math. Soc. 69 (1963), 83-86
DOI: https://doi.org/10.1090/S0002-9904-1963-10869-1
MathSciNet review: 0152504
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References [Enhancements On Off] (What's this?)

  • 1. Eckford Cohen, Binary congruences in algebraic number fields, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 120–122. MR 0079614
  • 2. J. T. Cross, The number of solutions of certain types of congruences in algebraic number fields, (to appear).
  • 3. G. Frattini, Intorno ad un teorema di Lagrange, Atti Reale Accad. Lincei Rend. 1 (1885), 136-142.
  • 4. H. Davenport and H. Hasse, Die Nullstellen der Kongruenz-zetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1935), 151-182.
  • 5. Emma Lehmer, On the number of solutions of 𝑢^{𝑘}+𝐷≡𝑤²(\mod𝑝), Pacific J. Math. 5 (1955), 103–118. MR 0067918
  • 6. Yu. I. Manin, On cubic congruences to a prime modulus, Amer. Math. Soc. Transl. (2) 13 (1960), 1–7. MR 0112865
  • 7. H. S. Vandiver, On the number of solutions of certain non-homogeneous trinomial equations in a finite field, Proc. Nat. Acad. Sci. U. S. A. 31 (1945), 170–175. MR 0012089


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1963-10869-1