Waring's conjecture

Waring's conjecture is a hypothesis given, without proof, by the English mathematician Edward Waring (1734–1798) in his Meditationes algebraicae (1770). It states that for every number k, there is another number s such that every natural number can be represented as the sum of s kth powers. For example, every natural number can be written as a sum of 4 squares, 9 cubes and so on. Waring's conjecture was first proved in full by David Hilbert in 1909.