Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
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Yasutsugu Fujita
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Maohua Le
Abstract
Let D be a nonsquare integer, and let k be an integer with |k| ≥ 1 and gcd(D, k) = 1. In the part I of this paper, using some properties on the representation of integers by binary quadratic primitive forms with discriminant 4D, M.-H. Le gave a series of explicit formulas for the integer solutions (x, y, z) of the equation x2 – Dy2 = kz, gcd(x, y) = 1, z > 0 for 2 ∤ k or |k| is a power of 2. In this part, we give similar results for the other cases of k.
Acknowledgement
The authors thank the referees for their careful reading and pertinent suggestions.
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Communicated by István Gaál
References
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Artikel in diesem Heft
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
