X-Nico

Sums of powers

Waring's problem asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s k^th powers of natural numbers.

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Faulhaber's formula expresses $1^k\; +\; 2^k\; +\; 3^k\; +\; \backslash cdots\; +\; n^k$ as a polynomial in n.

see also