Definition of Diophantine. Meaning of Diophantine. Synonyms of Diophantine

Here you will find one or more explanations in English for the word Diophantine. Also in the bottom left of the page several parts of wikipedia pages related to the word Diophantine and, of course, Diophantine synonyms and on the right images related to the word Diophantine.

Definition of Diophantine

Diophantine
Diophantine Di`o*phan"tine, a. Originated or taught by Diophantus, the Greek writer on algebra. Diophantine analysis (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x^2 + y^2 an exact square.

Meaning of Diophantine from wikipedia

- in Wiktionary, the free dictionary. Diophantine approximation Diophantine equation Diophantine quintuple Diophantine set This disambiguation page lists...
- In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only...
- In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became...
- In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk) = 0 (usually abbreviated P(x, y) = 0) where P(x, y) is a...
- In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...
- can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through...
- In the study of Diophantine geometry, the square lattice of points with integer coordinates is often referred to as the Diophantine plane. In mathematical...
- is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite...
- Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations...
- input a Diophantine equation and always determine whether it has a solution in integers. The undecidability of the halting problem and the Diophantine problem...