%A Ionascu, Eugen J.
%A Bradford, Kyle
%D 2017
%T Unit Fractions in Norm-Euclidean Rings of Integers
%K
%X In this article we consider the Erdos-Straus conjecture in a more general setting. For instance, one can look at the diophantine equation 4/n = 1/a + 1/b + 1/c where n and a; b; c are Gaussian integers. The problem becomes as difficult as the original Erdos-Straus conjecture if we require that the solutions be in the first or third quadrant for every given n in the first quadrant different of 0, 1, i, or 1 + i. However, without any other restrictions on a, b and c, we show that solutions exist except for a finite set. We considered also the case of rings of integers of the norm-Euclidean quadratic fields.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/368
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 127-141%V 86
%N 1
%@ 0862-9544
%8 2017-01-11