Gallardo, Luis H.; Vaserstein, Leonid N. Constants as sums of polynomial cubes in characteristic 2. (English) Zbl 1308.11102 J. Comb. Number Theory 5, No. 1, 1-9 (2013). In a finite field \(\mathbb{F}_q\) any element can be represented as the sum of two squares or three cubes (except for \(q=4\)) of elements of \(\mathbb{F}_q\). The authors consider the similar problem of representing the elements of \(\mathbb{F}_q\) as the sums of squares or cubes of polynomials of one variable over \(\mathbb{F}_q\) when at least one of the polynomials is nonconstant.It is shown that for any \(q\) all elements of the finite field \(\mathbb{F}_q\) can be written as the sum of squares of at least three elements from \(\mathbb{F}_q[t]\). Also partial results are given for the representation as the sum of cubes of polynomials for the characteristic 2 case. Reviewer: Ayça Çeşmelioǧlu (Istanbul) MSC: 11T55 Arithmetic theory of polynomial rings over finite fields 11P05 Waring’s problem and variants 11T06 Polynomials over finite fields PDFBibTeX XMLCite \textit{L. H. Gallardo} and \textit{L. N. Vaserstein}, J. Comb. Number Theory 5, No. 1, 1--9 (2013; Zbl 1308.11102)