Diophantine equation

Noun

Diophantine equation (plural Diophantine equations)

1. A polynomial equation whose variables are only permitted to assume integer values.
   • Nevertheless, the fundamental idea of Skolem's method, the reduction of algebraic diophantine equations to exponential equations, has shown exceptional vitality in recent episodes of the theory of diophantine equations.1993, Ross Talent, Alf van der Poorten (translation editors), Vladimir G. Sprindžuk, Classical Diophantine Equations, Springer, Lecture Notes in Mathematics 1559, page viii
   • Based on lectures he^([Davenport]) gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.2005, Harold Davenport, edited by T. D. Browning, Analytic Methods for Diophantine Equations and Diophantine Inequalities, 2nd edition, Cambridge University Press, page i