Journal of Mathematical Sciences

, Volume 137, Issue 2, pp 4699–4715 | Cite as

On Waring’s problem (elementary methods)

  • Yu. V. Nesterenko


The paper deals with two elementary methods for solving Waring’s problem on the representation of numbers as a sum of equal exponents in powers of natural numbers. The first method is an elementary version of the original Hilbert’s proof, and the second one simplifies and makes more precise the elementary Linnik’s proof based on the estimate of the number of solutions of a certain system of Diophantine equations. Bibliography: 21 titles.


Positive Integer Nonnegative Integer Recurrent Equation Diophantine Equation Continue Fraction Expansion 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. V. Nesterenko
    • 1
  1. 1.Moscow Lomonosov State UniversityMoscowRussia

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