1. Reducible diophantine equations. The present paper will provide a general method for obtaining the complete parametric representation for the rational integer solutions of the multiplicative diophantine equation
1.1 ![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0008414X00030443/resource/name/S0008414X00030443_eqn01.gif?pub-status=live)
for some specified range of k, where the aijk,bijk are non-negative integers and the fki, hki are decomposable forms, that is to say they are integral irreducible homogeneous polynomials over the rational field R of degree k in k variables which can be written as the product of k linear forms.