IJPAM: Volume 55, No. 1 (2009)

SOLVING LINEAR DIOPHANTINE MATRIX EQUATIONS
USING THE SMITH NORMAL FORM (MORE OR LESS)

Raymond N. Greenwell$^1$, Stanley Kertzner$^2$
$^{1,2}$Department of Mathematics
Hofstra University
Hempstead, NY 11549, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Using a modification of the Smith normal form of a matrix, we give necessary and sufficient conditions for the integer matrix equation $AX=B$ to have an integer solution, and we provide an explicit formula for that solution. We provide an algorithm for generating the solution, and we also show how the solution can be generated with Maple.

Received: June 15, 2009

AMS Subject Classification: 15A06, 15A24, 15A36

Key Words and Phrases: matrix equations, linear systems, Smith normal form, Diophantine equations, integer solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 1