The Diophantine equation $x^2 + q^m =p^n$

DOI10.4064/aa-63-4-351-358zbMath0770.11020OpenAlexW992501131MaRDI QIDQ4695198

Nobuhiro Terai

Publication date: 17 June 1993

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/206526

zbMATH Keywords

ideal class groupexponential diophantine equationpositive integral solution

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Exponential Diophantine equations (11D61)

Related Items (14)

The diophantine equation \(a^ x+b^ y=c^ z\) ⋮ On the Diophantine equation \(x^2+b^m=c^n\) with \(a^2+b^4=c^2\) ⋮ On a result of Fujita and Le ⋮ An application of Frey's idea to exponential diophantine equations ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ On the generalized Ramanujan-Nagell equation \(x^2+(2c-1)^m=c^n\) ⋮ On Terai's conjecture ⋮ A note on the diophantine equation x 2 + b y = c z ⋮ A new conjecture concerning the Diophantine equation \(x^2+b^y=c^z\). ⋮ A note on Terai's conjecture concerning Pythagorean numbers ⋮ On the generalized Ramanujan-Nagell equation \(x^2 + b^m = c^n\) with \(a^2 + b^r = c^2\) ⋮ A note on Terai's conjecture concerning primitive Pythagorean triples ⋮ A note on the Diophantine equation \(x^2 + q^m = c^{2n}\) ⋮ On a conjecture on Pythagorean numbers

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