On the generalized Ramanujan-Nagell equation \(x^2+D=p^z\)

DOI10.1006/jnth.1999.2415zbMath0971.11018OpenAlexW2122072260MaRDI QIDQ1125385

Maohua Le, Clemens Heuberger

Publication date: 14 February 2000

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2415

zbMATH Keywords

exponential Diophantine equationexponential congruences

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (8)

On a conjecture of Iizuka ⋮ On the Diophantine equation \(NX^2 + 2^L3^M = Y^N\) ⋮ The exponential Diophantine equation \(x^y + y^x = y^2\) with \(xy\) odd ⋮ On the Diophantine equation \(nx^2+2^{2m}=y^n\) ⋮ A bound for the solutions of the Diophantine equation \(D_1x^2+D_2^m=4y^n\) ⋮ THE DIVISIBILITY OF THE CLASS NUMBER OF THE IMAGINARY QUADRATIC FIELD ⋮ On the Diophantine equation \(ax^2+by^2=ck^n\) ⋮ A note on the Diophantine equation \(x^2 + q^m = c^{2n}\)

Uses Software

• KANT/KASH

Cites Work

• On the Diophantine equation \(y^2=4q^n+4q+1\)
• KANT V4
• Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
• A note on the number of solutions of the generalized Ramanujan-Nagell equation $x²-D = k^n$
• The Diophantine equation $x^2+11=3^k$ and related questions.
• On a Pellian Equation Conjecture (II)
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