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, 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...

given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution...

five sextic equation for degree six septic equation for degree seven octic equation for degree eight A Diophantine equation is an equation where the unknowns...

Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where...

Claude Bachet. Diophantine equations have been studied for thousands of years. For example, the solutions to the quadratic Diophantine equation x2 + y2 = z2...

composite numbers. The Euclidean algorithm may be used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences according...

equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation...

be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a...

In mathematics, a polynomial Diophantine equation is an indeterminate polynomial equation for which one seeks solutions restricted to be polynomials in...

example, consider the equation x 2 = 2. {\displaystyle x^{2}=2.} This equation can be viewed as a Diophantine equation, that is, an equation for which only integer...

In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became...

the linear Diophantine equation, whereas Diophantus himself had been satisfied to give one particular solution of an indeterminate equation. Inasmuch as...

algebraic equation over the rationals. A Diophantine equation is a (usually multivariate) polynomial equation with integer coefficients for which one is...

Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood...

to America. Édouard Lucas formulated the cannonball problem as a Diophantine equation ∑ n = 1 N n 2 = M 2 {\displaystyle \sum _{n=1}^{N}n^{2}=M^{2}} or...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

in Wiktionary, the free dictionary. Diophantine approximation Diophantine equation Diophantine quintuple Diophantine set This disambiguation page lists...

identity for homogeneous polynomials in three indeterminates Diophantine equation – Polynomial equation whose integer solutions are sought Euclid's lemma – A...

class is the nature of the resulting equation, which is a linear Diophantine equation in two unknowns. Most members of the class are determinate, but some...

Diophantus and Diophantine Equations is a book in the history of mathematics, on the history of Diophantine equations and their solution by Diophantus...

the equation a2 + b2 = c2 is a Diophantine equation. Thus Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation. There...

In mathematics, a Thue equation is a Diophantine equation of the form f ( x , y ) = r , {\displaystyle f(x,y)=r,} where f {\displaystyle f} is an irreducible...

Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations...

applications in the study of Diophantine equations. The 2022 Fields Medal was awarded to James Maynard for his work on Diophantine approximation. Given a real...

the Diophantine equation x! + A = y2", Nieuw Archief voor Wiskunde, 14 (3): 321–324, MR 1430045 Luca, Florian (2002), "The Diophantine equation P(x)...

both sides by abc shows that the optic equation is equivalent to a Diophantine equation (a polynomial equation in multiple integer variables). All solutions...

not a Diophantine equation has any solution at all". MRDP uses the undecidability proof of Turing: "... the set of solvable Diophantine equations is an...

for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ax + by = c where x and y are...

solutions to an equation using Vieta's formulas. Vieta jumping is a classical method in the theory of quadratic Diophantine equations and binary quadratic...