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April 2021 On the solutions of certain Lebesgue–Ramanujan–Nagell equations
Kalyan Chakraborty, Azizul Hoque, Richa Sharma
Rocky Mountain J. Math. 51(2): 459-471 (April 2021). DOI: 10.1216/rmj.2021.51.459

Abstract

We completely solve the Diophantine equation x2+2k1119m=yn in integers x,y1; k,,m0 and n3 with gcd(x,y)=1, except the case 2|k, 2m and 5|n. We use this result to recover some earlier results in the same direction.

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Kalyan Chakraborty. Azizul Hoque. Richa Sharma. "On the solutions of certain Lebesgue–Ramanujan–Nagell equations." Rocky Mountain J. Math. 51 (2) 459 - 471, April 2021. https://doi.org/10.1216/rmj.2021.51.459

Information

Received: 12 October 2020; Revised: 23 October 2020; Accepted: 24 October 2020; Published: April 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.459

Subjects:
Primary: 11D41 , 11D61
Secondary: 11R29

Keywords: Diophantine equation , integer solution , Lucas sequences , primitive divisors , S-integers

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 2 • April 2021
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