A special case of the solution to this problem can be proved using Minkowski's theorem; that special case is the Lagrange   four-squares theorem.
This question was answered a rmatively by Hilbert in 1909, but his proof was nonconstructive. Liouville showed that the fourth power case for this ques- tion had an upper bound of 53; Hardy and Littlewood showed that it was 19 for all su ciently large integers, and that solution was extended to all integers in 1986. A special case of the solution to this problem can be proved using Minkowski's theorem; that special case is the Lagrange   four-squares theorem. For ten points, identify this mathematical problem which asked of every natural number k whether there was a number s such that every integer can be written as at most s kth powers.
This question was answered a rmatively by Hilbert in 1909, but his proof was nonconstructive.
Waring's problem [accept Hilbert-Waring theorem]