Waring’s problem for cubes

  • Melvyn B. Nathanson
Part of the Graduate Texts in Mathematics book series (GTM, volume 164)


In his book Meditationes Algebraicae, published in 1770, Edward Waring stated without proof that every nonnegative integer is the sum of four squares, nine cubes, 19 fourth powers, and so on. Waring’s problem is to prove that, for every k ≥ 2, the set of nonnegative kth powers is a basis of finite order.


Nonnegative Integer Polynomial Identity Chinese Remainder Theorem Congruence Class Implied Constant 


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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Melvyn B. Nathanson
    • 1
  1. 1.Department of MathematicsLehman College of the City University of New YorkBronxUSA

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