Waring's problem for integral quaternions
The classical Waring's problem states that for every positive integer \(m\) it is always possible to find a positive integer \(g\) such that any positive integer can be written as the sum of \(g\) \(m\)-th powers. This paper proves that this result also holds true in the context of Lipschitz quaternions, i.e., in the set \[ \mathbb{L}=\{a+bi+cj+dk:a,b,c,d\in\mathbb{Z}\}. \]
scientific article; zbMATH DE number 6939361
scientific article