On numbers of the form n = x(2) + ny(2) and the hecke groups h(root n)

Abstract

We consider the Hecke groups H(root N), N >= 2 integer, to get some results about the problem when a natural number n can be represented in the form n = x(2) + Ny(2). Given a natural number n, we give an algorithm that computes the integers x and y satisfying the equation n = x(2) + Ny(2) for all N >= 2. (c) 2010 Elsevier Inc. All rights reserved.