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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 soluble effectively: there is an explicit bound on the solutions ''x'', ''y'' of the form where constants ''C''1 and ''C''2 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. ==Solving Thue equations== Solving a Thue equation can be described as an algorithm ready for implementation in software. In particular, it is implemented in the following computer algebra systems: * in PARI/GP as functions ''thueinit()'' and ''thue()''. * in Magma computer algebra system as functions ''ThueObject()'' and ''ThueSolve()''. * in Mathematica through ''Reduce'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thue equation」の詳細全文を読む スポンサード リンク
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