Diophantine equation

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Diophantine equation

(mathematics)
Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions.

References in periodicals archive ?
Clay Mathematics Institute Summer School Arithmetic Geometry (2006: Gottingen, Germany).
Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this book introduces readers to modern techniques and outstanding conjectures at the interface of number theory and algebraic geometry.
Higher Genus Curves in Mathematical Physics and Arithmetic Geometry
The proceedings of a January 2016 session in Seattle presents 13 papers on the role of higher genus curves in both mathematical physics and arithmetic geometry. Among their topics are a lower bound for the number of finitely maximal Cp-actions on a compact oriented surface, rational points in the moduli space of genus two, Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited, extending Runge's method for integral points, and syzygy divisors on Hurwitz spaces.
Arithmetic geometry and characteristic p methods took up the final week.
Conrad and Prasad present readers with a comprehensive examination of algebraic and arithmetic geometry and the production of imperfect fields.
AMS Special Session on Computational Arithmetic Geometry (2006: San Francisco, CA) Ed.
From June 3-8, 2006, mathematicians lectured physicists on modular and quasi-modular forms in string theory and related themes, while physicists enlightened mathematicians on aspects of mirror symmetry and topological string theory that have inspired new developments in number theory, algebraic and arithmetic geometry, toric geometry, Riemann surface theory, and infinite dimensional Lie algebras.
Moduli spaces and arithmetic geometry; proceedings.