Squares in number theory | Unsolved problems in number theory | Additive number theory | Mathematical problems

Waring's problem

In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward Waring, after whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its own Mathematics Subject Classification, 11P05, "Waring's problem and variants". (Wikipedia).

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Harold Davenport | G. H. Hardy | Pierre de Fermat | R. K. Rubugunday | Arthur Wieferich | Joseph Liouville | Arithmetica | Waring–Goldbach problem | David Hilbert | Subbayya Sivasankaranarayana Pillai | Otto Toeplitz | Ivan M. Niven | Fermat polygonal number theorem | Fractional part | Lagrange's four-square theorem | Edward Waring | Hans Rademacher | Natural number | Diophantus | Leonard Eugene Dickson | Schnirelmann density | Kurt Mahler | Number theory | Mathematics Subject Classification | Chen Jingrun | John Edensor Littlewood | Joseph-Louis Lagrange | Sums of three cubes | Leonhard Euler | Subset sum problem