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Sums of Squares Coprime in Pairs

Jörg Brüdern (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.

Sums of squares in rings of integers with 2 inverted

Gaël Collinet (2016)

Acta Arithmetica

We prove that in a ring of S-integers containing 1/2, any totally positive element is a sum of five squares. We also exhibit examples of such rings where some totally positive elements cannot be written as the sum of four squares.

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