A chemical equation as a representation of a class of linear Diophantine equations and a system of homogeneous linear equations

Abstract

A chemical equation, comprising nelements interspersed among mspecies (reactants + products) and where the stoichiometric coefficients are represented by algebraic symbols, is shown to be equivalent to a class of linear Diophantine equations as well as a system of khomogeneous linear equations in munknowns, where k^ n.The use of conservation conditions for the elements in the chemical equation affords a non‐conventional approach for the generation of some of the integral solution sets of the Diophantine equations and the integral solutions of the system of homogeneous linear equations.