Thue equation
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For other theorems named after Axel Thue, see Thue's theorem (disambiguation).
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 Thue equation has finitely many solutions in integers x and y.[1]
[edit] Solving Thue equations
Solving a Thue equation can be described as an algorithm[2] ready for implementation in software. In particular, it is implemented in the following computer algebra systems:
- in PARI/GP as functions thueinit() and thue().
[edit] References
- ^ A. Thue (1909). "Über Annäherungswerte algebraischer Zahlen". Journal für die reine und angewandte Mathematik 135: 284–305. http://resolver.sub.uni-goettingen.de/purl?PPN243919689_0135.
- ^ N. Tzanakis and B. M. M. de Weger (1989). "On the practical solution of the Thue equation". Journal of Number Theory 31 (2): 99–132. doi:10.1016/0022-314X(89)90014-0.
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