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.]

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]
References in periodicals archive ?
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.
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.
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.
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
Hence we can write the equation 4n+8=2p as 4n - 2p= - 8 which is nothing but a diophantine equation.
We search for nonzero integral triples (x, y, z) satisfying the quartic Diophantine equation 2[x.
Although the phrases step function and Diophantine equation will not come up at the elementary level, it is important for elementary mathematics teachers to lay the foundation in preparation for when students do learn about such topics.