Editing Lagrange's four-square theorem (section)

==Further refinements==
Lagrange's four-square theorem can be refined in various ways. For example, [[Zhi-Wei Sun]]<ref>{{harvnb|Sun|2017}}.</ref> proved that each natural number can be written as a sum of four squares with some requirements on the choice of these four numbers.

One may also wonder whether it is necessary to use the entire set of square integers to write each natural as the sum of four squares. [[Eduard Wirsing]] proved that there exists a set of squares {{mvar|S}} with <math>|S| = O(n^{1/4}\log^{1/4} n)</math> such that every positive integer smaller than or equal to {{mvar|n}} can be written as a sum of at most 4 elements of  {{mvar|S}}.<ref>{{harvnb|Spencer|1996}}</ref>