Sommes de bicarrés dans \(\mathbb Z[\sqrt{-1}]\) et \(\mathbb Z[\sqrt[3]{1}]\). (Q1139630)

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 \textit{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.