Diophantine equations | Theorems in number theory

Thue equation

In mathematics, a Thue equation is a Diophantine equation of the form ƒ(x,y) = r, where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue who in 1909 proved a theorem, now called Thue's theorem, that a Thue equation has finitely many solutions in integers x and y. The Thue equation is solvable effectively: there is an explicit bound on the solutions x, y of the form where constants C1 and C2 depend only on the form ƒ. A stronger result holds, that if K is the field generated by the roots of ƒ then the equation has only finitely many solutions with x and y integers of K and again these may be effectively determined. (Wikipedia).

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Related pages

Axel Thue | Diophantine equation | Effective results in number theory | Irreducible polynomial | Mathematics | Rational number | Roth's theorem | Klaus Roth | PARI/GP | Uniform boundedness conjecture for rational points | Theorem | Computer algebra system | Discriminant | Carl Ludwig Siegel | Alan Baker (mathematician)