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In number theory, Waring–Hilbert’s theorem guarantees that for each k there is an integer h ≥ 0 so that, for every non-negative integer n there are non-negative integers a1,a2,...,ak such that ak 1 + ak 2 + ··· + ak h = n. In this thesis the problem will first be proved in the specific case where k = 2. Then the proof of the general case due to Yuri Linnik will be given. The notion of Shnirelman d
