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On the 4-power stufe of a field

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Abstract

Define the 4-powers 4 (k) of a fieldk to be the least positive integers for which the equation −1=a 41 +…+a 4s is solvable ink (if at all). We determines 4 (k) whenk is a Galois field and prove some results abouts 4 (k) whenk is an imaginary quadratic field.

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References

  1. Birch B.J.,Waring's problem in algebraic number fields, Proc. Camb. Phil. Soc.,57 (1961), 449–459.

    Article  MATH  MathSciNet  Google Scholar 

  2. Davenport H.,On Waring's problem for fourth powers, Annals of Math.,40 (1939), 731–747.

    Article  MathSciNet  Google Scholar 

  3. Dickson L.E.,Cyclotomy, higher congruences and Waring's problem, Amer. J. Math.,57 (1935), 391–424.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Panjab University, 160014, Chandigarh

    J. C. Parnami, M. K. Agrawal & A. R. Rajwade

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  1. J. C. Parnami
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  2. M. K. Agrawal
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  3. A. R. Rajwade
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Parnami, J.C., Agrawal, M.K. & Rajwade, A.R. On the 4-power stufe of a field. Rend. Circ. Mat. Palermo 30, 245–254 (1981). https://doi.org/10.1007/BF02844309

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  • DOI: https://doi.org/10.1007/BF02844309

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