For every integer k greater than or equal to two, there exists a finite number g(k) such that every natural number can be written as the sum of at most g(k) k-th powers. It resolves Waring's problem, proved in full generality by David Hilbert.
Facts
StatementFor every positive integer k there exists a finite number g(k) such that every natural number is the sum of at most g(k) k-th powers of natural numbers, resolving Waring's 1770 conjecture in the affirmative. 2 Classification
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Sources
1. Wikipedia: Waring's problem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
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.
2. Hilbert-Waring Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
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.
lead paragraph, fourth sentence
Its affirmative answer, known as the Hilbert-Waring theorem, was provided by Hilbert in 1909.
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