On the generalized Ramanujan-Nagell equation \(x^2 + b^m = c^n\) with \(a^2 + b^r = c^2\)

DOI10.55937/sut/1654320039OpenAlexW4285608892MaRDI QIDQ2092318

Nobuhiro Terai, Yudai Suenaga, Saya Nakashiki

Publication date: 2 November 2022

Published in: SUT Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.55937/sut/1654320039

zbMATH Keywords

Jeśmanowicz' conjectureZsigmondy's theoremgeneralized Ramanujan-Nagell equation

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items

A note on the solution to the generalized Ramanujan-Nagell equation \(x^2+(4c)^y=(c+1)^z\)

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The diophantine equation \(x^ 2 + 2^ k = y^ n\)
• A note on Terai's conjecture concerning Pythagorean numbers
• On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
• A new conjecture concerning the Diophantine equation \(x^2+b^y=c^z\).
• On the equation \(x^2 + 2^a \cdot 3^b = y^n\)
• On the Diophantine equation \(x^2+b^m=c^n\) with \(a^2+b^4=c^2\)
• On the generalized Ramanujan-Nagell equation \(x^2+(2c-1)^m=c^n\)
• A note on the Diophantine equation \(x^2 + q^m = c^{2n}\)
• On Terai's conjecture concerning Pythagorean numbers
• Sums of two $S$-units via Frey-Hellegouarch curves
• A note on the diophantine equation x 2 + b y = c z
• ON THE DIOPHANTINE EQUATION x² + 2^a · 5^b = yⁿ
• On the diophantine equation $x^2 + b^y = c^z$
• A NOTE ON THE DIOPHANTINE EQUATION
• The Diophantine equation $x^2 + q^m =p^n$
• A note on the diophantine equation $x² + b^y = c^z$
• A NOTE ON THE DIOPHANTINE EQUATION
• On Terai's conjecture