turkmath.org

Waring's problem is one of the famous questions in additive number theory stating that for each k ? 2, there is some constant s(k) such that every integer is the sum of at most s k th 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 a?rmative answer, known as the Hilbert-Waring theorem, was provided by Hilbert in 1909. In this talk, I will give a brief history of Waring's problem and recent advancements over it. I will also discuss related results of mine as time permits.