## Rocky Mountain Journal of Mathematics

### A Generalization of a Theorem of Cohn on the Equation $x^3-Ny^2=\pm1$

#### Article information

Source
Rocky Mountain J. Math. Volume 31, Number 2 (2001), 503-509.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.rmjm/1181070209

Digital Object Identifier
doi:10.1216/rmjm/1020171571

Mathematical Reviews number (MathSciNet)
MR1840950

Zentralblatt MATH identifier
0989.11016

Subjects
Primary: 11D25: Cubic and quartic equations
Secondary: 11J86: Linear forms in logarithms; Baker's method

#### Citation

Luca, F.; Walsh, P.G. A Generalization of a Theorem of Cohn on the Equation $x^3-Ny^2=\pm1$. Rocky Mountain J. Math. 31 (2001), no. 2, 503--509. doi:10.1216/rmjm/1020171571. http://projecteuclid.org/euclid.rmjm/1181070209.

#### References

• M.A. Bennett and P.G. Walsh, The Diophantine equation $b^2X^4-dY^2=1$, Proc. Amer. Math. Soc. 127 (1999),
• J.H.E. Cohn, The Diophantine equations $x^3=Ny^2\pm1$, Quart. J. Math. Oxford 42 (1991), 27-30.
• --------, The Diophantine equation $x^4-Dy^2=1$, II, Acta Arith. 78 (1997), 401-403.
• D.H. Lehmer, An extended theory of Lucas functions, Ann. Math. 31 (1930), 419-448.
• R.J. Stroeker, On the Diophantine equation $x^3-Dy^2=1$, Nieuw Arch. Wisk. 24 (1976), 231-255.
• N. Tzanakis, Solving elliptic Diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations, Acta Arith. 75 (1996), 165-190.
• P.G. Walsh, Diophantine equations of the form $aX^4-bY^2=\pm1$, Proc. ICM Satellite Conf. in Graz on Analytic Number Theory and Diophantine Analysis (R. Tichy, ed.), 1998, to appear.
• --------, A note on a theorem of Ljunggren and the Diophantine equations $x^2-kxy^2+y^4=1,4$, Arch. Math. 73 (1999), 119-125.
• --------, The Diophantine equation $X^2-db^2Y^4=1$, Acta Arith. 87 (1998), 179-188.