{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. [1913 Webster]
The Collaborative International Dictionary of English. 2000.
Diophantine — means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: Diophantine approximation Diophantine equation Diophantine set This disambiguation page lists articles associated with the same title. If an … Wikipedia
Diophantine analysis — Diophantine Di o*phan tine, a. Originated or taught by Diophantus, the Greek writer on algebra. [1913 Webster] {Diophantine analysis} (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that… … The Collaborative International Dictionary of English
Diophantine analysis — noun (mathematics) The part of algebra concerned with finding particular rational values for general expressions under a surd form • • • Main Entry: ↑Diophantine … Useful english dictionary
Diophantine equation — In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for… … Wikipedia
Diophantine set — 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 polynomial with integer coefficients. A Diophantine set is a subset S of Nj [1] so that for some… … Wikipedia
Diophantine approximation — In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. The absolute value of the difference between the real number to be approximated and… … Wikipedia
Diophantine geometry — In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of… … Wikipedia
diophantine equation — /duy euh fan tuyn, teen, fan tn/, Math. an equation involving more than one variable in which the coefficients of the variables are integers and for which integral solutions are sought. [1925 30; named after Diophantus, 3rd century A.D. Greek… … Universalium
Diophantine — adjective Of or pertaining to Diophantus, the Greek mathematician … Wiktionary
diophantine — di·o·phan·tine … English syllables
