## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 18, Issue 2 (2006), 135-141.

### Integer Solutions of Linear Diophantine Equations Form a Group

#### Abstract

It is shown that the set of integer solutions of a single Diophantine equation, or of several simultaneous linear Diophantine equations, in an arbitrary number of variables, say $n$, is a group with respect to a suitably defined binary operation. Further, the aforesaid group is the direct sum of $n$ cyclic groups.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 18, Issue 2 (2006), 135-141.

**Dates**

First available in Project Euclid: 3 August 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1564797713

**Digital Object Identifier**

doi:10.35834/2006/1802135

**Zentralblatt MATH identifier**

1148.11014

**Subjects**

Primary: 11D04: Linear equations

#### Citation

Choudhry, Ajai. Integer Solutions of Linear Diophantine Equations Form a Group. Missouri J. Math. Sci. 18 (2006), no. 2, 135--141. doi:10.35834/2006/1802135. https://projecteuclid.org/euclid.mjms/1564797713