by

Ciro Santilli (@cirosantilli, 36)

Waring's problem for squares

4 squares are sufficient by Lagrange's four-square theorem.

3 is not enough by Legendre's three-square theorem.

The subsets reachable with 2 and 3 squares are fully characterized by Legendre's three-square theorem and

Table of contents

Lagrange's four-square theorem (Every natural number is a sum of four squares, 1770)

 1  0 

Legendre's three-square theorem (iff not of form $4^{a} (8 b + 7)$ , 1770)

 1  0 

Sum of two squares theorem

 1  0 

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