Waring’s Problem

Anatolij A. Karatsuba and Melvyn B. Nathanson
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Anatolij A. Karatsuba: Steklov Mathematical Institute
Melvyn B. Nathanson: School of Mathematics, Institute for Advanced Study

Chapter Chapter XI in Basic Analytic Number Theory, 1993, pp 160-180 from Springer

Abstract: Abstract In this chapter we study the representation of a natural number N as the sum of a fixed number of fixed powers of natural numbers, i.e. the question of the solvability in natural numbers x 1, x 2,…,x k of the equation 1 $$ x_1^n + x_2^n + \ldots + x_k^n = N $$ where n ≥3 and k = k(n) (Waring’s problem). Waring’s problem generalizes Lagrange’s theorem that every natural number is the sum of four squares.

Date: 1993
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DOI: 10.1007/978-3-642-58018-5_11

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