Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.6 |

Department of Mathematics

Indian Institute of Technology

Hauz Khas

New Delhi - 110016

India

Sujith Vijay

Department of Mathematics

Rutgers University -- New Brunswick

Piscataway, NJ 08854

USA

**Abstract:**

Given relatively prime and positive integers
,
let denote the set of nonnegative integers representable
by the form
, and let
denote the positive integers in . Let
denote the set of all
positive integers not in for which
is contained in
. The purpose
of this article is to determine an algorithm which can be used to
obtain the set
in the three variable case. In
particular, we show that the set
has
at most two elements. We also obtain a formula for
,
the largest integer not representable by the form
with the 's nonnegative integers.

Received December 20 2005;
revised version received September 12 2006.
Published in *Journal of Integer Sequences* September 12 2006.

Return to