The Diophantine equation X² - db²Y⁴ = 1

 Access to full text

 Full (PDF)

1. [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Proc. Cambridge Philos. Soc. 65 (1969), 439-444. Zbl0174.33803
2. [2] M. A. Bennett and P. G. Walsh, The Diophantine equation b²X⁴ - dY² = 1, Proc. Amer. Math. Soc., to appear. Zbl0980.11021
3. [3] J. H. Chen and P. M. Voutier, A complete solution of the Diophantine equation x² + 1 = dy⁴ and a related family of quartic Thue equations, J. Number Theory 62 (1997), 71-99. Zbl0869.11025
4. [4] J. H. E. Cohn, The Diophantine equation x⁴ - Dy² = 1, II, Acta Arith. 78 (1997), 401-403. Zbl0870.11018
5. [5] M. Langevin, Cas d'inégalité pour le théorème de Mason et applications de la conjecture (abc), C. R. Acad. Sci. Paris Sér. I 317 (1993), 441-444. 
6. [6] D. H. Lehmer, An extended theory of Lucas' functions, Ann. of Math. 31 (1930), 419-448. Zbl56.0874.04
7. [7] W. Ljunggren, Einige Eigenschaften der Einheiten reeller quadratischer und rein-biquadratischer Zahlkörper mit Anwendung auf die Lösung einer Klasse unbestimmter Gleichungen vierten Grades, Skr. Norske Vid.-Akad. Oslo 1936, no. 12, 1-73. 
8. [8] W. Ljunggren, Zur Theorie der Gleichung x² + 1 = Dy⁴, Avh. Norske Vid. Akad. Oslo 1942, no. 5, 1-26. 
9. [9] W. Ljunggren, Über die Gleichung x⁴ - Dy² = 1, Arch. Math. Naturv. 45 (1942), no. 5, 61-70. Zbl68.0069.01
10. [10] M. Mignotte et A. Pethő, Sur les carrés dans certaines suites de Lucas, J. Théor. Nombres Bordeaux 5 (1993), 333-341. Zbl0795.11007
11. [11] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, New York, 1986. Zbl0606.10011
12. [12] P. G. Walsh, A note on a theorem of Ljunggren and the Diophantine equations x² - kxy² + y⁴ = 1,4, Arch. Math. (Basel), to appear. Zbl0941.11012