Representation of Integers Using a^2 + b^2 - dc^2

摘要

A positive integer d is called special if every integer m can be expressed as a2 + b2 a?? dc2 for some nonzero integers a,b,c. A necessary condition for special numbers was recently given by Nowicki, and in this paper we prove its sufficiency. Thus, we give a complete characterization for special numbers.