Revoy, Ph. Sommes de bicarrés dans \(\mathbb Z[\sqrt{-1}]\) et \(\mathbb Z[\sqrt[3]{1}]\). (French) Zbl 0434.12001 Enseign. Math., II. Sér. 25, 257-260 (1979). 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. Reviewer: M. M. Dodson (Heslington) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 11R04 Algebraic numbers; rings of algebraic integers 11P05 Waring’s problem and variants Keywords:Gaussian integer; sum of biquadrates Citations:Zbl 0028.00803 PDFBibTeX XMLCite \textit{Ph. Revoy}, Enseign. Math. (2) 25, 257--260 (1979; Zbl 0434.12001)