Diophantine equation


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Diophantine equation

n.
An algebraic equation with two or more variables whose coefficients are integers, studied to determine all integral solutions.

[After Diophantus, third-century ad Greek mathematician.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Diophantine equation

(ˌdaɪəʊˈfæntaɪn)
n
(Mathematics) (in number theory) an equation in more than one variable and with integral coefficients, for which integral solutions are sought
[C18: after Diophantus, Greek mathematician of the 3rd century ad]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
The inner loop was designed using linear algebraic method via solving a set of Diophantine equation, while the outer loop was designed using LQG controller.
The specialization of the polynomial f (a, x) with a 2 Q is irreducible if and only if a is not one of the following forms with a rational solution (A, B) of the Diophantine equation [A.sup.2] - 2[B.sup.2] = 1:
Spock: But again Feinstein's argument would not apply to this Diophantine equation, precisely because this Diophantine equation can be reduced via the Euclidean algorithm to the equation,
Both methods, the standard PSO algorithm and the proposed modification PSO + GI algorithm, are tested on the Diophantine equation solver task (see Table 1 in Section 5.1 for test equations).
A note on the Diophantine equation [x.sup.2] + [q.sup.m] = [c.sup.2n] Mou-Jie DENG Communicated by Shigefumi MORI, M.J.A.
By solving the Diophantine equation (11), the polynomials R and S can be obtained.
By Diophantine equation, we mean that Pythagorean triples a,b,c have been substituted with natural numbers such that for any n2, the equation (5) can be expressed as:
Since Peter had stumbled across 33 + 43 + 53 = 63, I looked for other solutions to the Diophantine equation [a.sup.3] + [b.sup.3] + [c.sup.3] = [d.sup.3], and found that it was Euler who discovered the complete solution, with Ramanujan later finding a simpler form (see Berndt & Bhargava, 1993).
Some groups considered equation (1) as a diophantine equation, determined all non-negative solutions and proved that these solutions are not realisable.
The general solution of the Diophantine equation [x.sup.2] - [2y.sup.2] = -1 is
The only solutions to this Diophantine equation are x - x' = sa + bt, y - y' = sb - at for t [member of] Z.
In [6], Stroeker investigated the Diophantine equation