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 kth powers of natural numbers. 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."