The name of the British mathematician Edward Waring is associated with the following problem: given an integer n, can every integer N be written as a sum of nth powers of strictly positive integers? If so, what is the minimum number of powers required, usually denoted by g(n)?
Waring's question was probably inspired by Lagrange's four-square theorem, proved in 1770 by Joseph Louis Lagrange (1736–1813): Every integer N can be written as a sum of at most four integer squares.
For example, 10 = 32 + 12, while 2,023 = 432 + 132 + 22 + 12. In the notation above, Lagrange's four-square theorem says that g(2) = 4.
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