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Sommes de bicarrés dans \(\mathbb Z[\sqrt{-1}]\) et \(\mathbb Z[\sqrt[3]{1}]\). (French) Zbl 0434.12001

The author shows that every Gaussian integer of the form \(a + 24bi\) is the sum of at most 12 biquadrates and using an observation of I. Niven [Bull. Am. Math. Soc. 47, 923–926 (1941; Zbl 0028.00803)] he deduces that every Gaussian integer which is the sum of biquadrates is the sum of at most 12. It is also shown that every integer in \(\mathbb Z[p]\), where \(p^2+p+1=0\), is the sum of at most 12 biquadrates. The proofs rely on a number of identities.

MSC:

11R04 Algebraic numbers; rings of algebraic integers
11P05 Waring’s problem and variants

Citations:

Zbl 0028.00803
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