Editing Lagrange's four-square theorem (section)

==Uniqueness==
The sequence of positive integers which have only one representation as a sum of four squares of non-negative integers (up to order) is:

:1, 2, 3, 5, 6, 7, 8, 11, 14, 15, 23, 24, 32, 56, 96, 128, 224, 384, 512, 896 ... {{OEIS|A006431}}.

These integers consist of the seven odd numbers 1, 3, 5, 7, 11, 15, 23 and all numbers of the form <math>2(4^k),6(4^k)</math> or <math>14(4^k)</math>.

The sequence of positive integers which cannot be represented as a sum of four ''non-zero'' squares is:

:1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41, 56, 96, 128, 224, 384, 512, 896 ... {{OEIS|A000534}}.

These integers consist of the eight odd numbers 1, 3, 5, 9, 11, 17, 29, 41 and all numbers of the form <math>2(4^k),6(4^k)</math> or <math>14(4^k)</math>.