Waring's problem

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Waring's problem concerns the determination of what is the maximum amount of $n$th powers needed to sum up to any integer. For example, no more than 9 cubes are ever necessary to add up to any integer: 2025 could be expressed as $253\times 2^{3}+1^{3}$, but it is much more easily expressed as the sum of the first nine cubes.