All solutions to Thomas¿ family of Thue equations over imaginary quadratic number fields

• Autores: Clemens Heuberger
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 9, 2006, págs. 980-998
• Idioma: inglés
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• Resumen

  • We completely solve the family of relative Thue equations where the parameter t, the root of unity µ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t|=53 and Baker¿s method combined with a computer search using continued fractions for the remaining values of t.

    x3-(t-1)x2y-(t+2)xy2-y3=µ,