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Complete Solution of the Diophantine EquationX2+1=dY4and a Related Family of Quartic Thue Equations by Chen Jian Hua; Paul Voutier is a Mathematics article available to read on EtoBox.
What is Complete Solution of the Diophantine EquationX2+1=dY4and a Related Family of Quartic Thue Equations about?
In this paper, we use the method of Thue and Siegel, based on explicit Pade approximations to algebraic functions, to completely solve a family of quartic Thue equations. From this result, we can also solve the diophantine equation in the title. We prove that this equation has at most one solution in positive integers when d 3. Moreover, when such a solution exists, it is of the form (u, -v) where (u, v) is the fundamental solution of X 2 +1=dY 2 . ## 1997 Academic Press Theorem A (Ljunggren [8]). If the fundamental unit of the quadratic field Q(d) is not also the fundamental unit of the ring Z[d], then equation (1.1) has at most two possible solutions in positive integers, and these can be found by a finite algorithm.
Who reads Complete Solution of the Diophantine EquationX2+1=dY4and a Related Family of Quartic Thue Equations?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Chen Jian Hua; Paul Voutier
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)
- Published
- 1997
- Language
- EN
- Field
- Mathematics (Physical Sciences)