<abstract xmlns="http://www.w3.org/1999/xhtml">We give a brief survey on some classical and recent results concerning the generalized Lebesgue-Ramanujan-Nagell equation. Moreover, we solve completely the equation <italic>x</italic>2 + 11<italic>a</italic> 17<italic>b</italic> = <italic>yn</italic> in nonnegative integer unknowns with <italic>n</italic> ≧ 3 and gcd(<italic>x, y</italic>) = 1.</abstract>

We give a brief survey on some classical and recent results concerning the generalized Lebesgue-Ramanujan-Nagell equation. Moreover, we solve completely the equation x2 + 11a 17b = yn in nonnegative integer unknowns with n ≧ 3 and gcd(x, y) = 1.

On Generalized Lebesgue-Ramanujan-Nagell Equations

Institute of Mathematics University of Debrecen H-4010 Debrecen, P.O. Box 12 Hungary

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On Generalized Lebesgue-Ramanujan-Nagell Equations"}

We give a brief survey on some classical and recent results concerning the generalized Lebesgue-Ramanujan-Nagell equation. Moreover, we solve completely the...

On Generalized Lebesgue-Ramanujan-Nagell Equations

Published Online: Dec 10, 2014

Page range: 51 - 71

Received: Jan 01, 2014

Accepted: Feb 01, 2014

DOI: https://doi.org/10.2478/auom-2014-0006

Keywords
Generalized Lebesgue-Ramanujan-Nagell equations, Primitive divisor theorem

© 2014 Attila Bérczes and István Pink

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Generalized Lebesgue-Ramanujan-Nagell Equations

Published Online: Dec 10, 2014

Page range: 51 - 71

Received: Jan 01, 2014

Accepted: Feb 01, 2014

DOI: https://doi.org/10.2478/auom-2014-0006

KeywordsGeneralized Lebesgue-Ramanujan-Nagell equations, Primitive divisor theorem

© 2014 Attila Bérczes and István Pink

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Generalized Lebesgue-Ramanujan-Nagell equations, Primitive divisor theorem