A parametric family of quartic Thue equations

Abstract

In this paper,we give all primitive solutions of a parameterized family of quartic Thue equations:

　　　　　 x^4-4c{x}^{3}y+(6c+2)x^2{y}^2+4cx{y}^3+y^4=96c+169,c>0.

Key words： Extension of classical Legendre's theorem; Baker-Wüstholz's theorem; Thue equation

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