Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 557-561

PROOF OF THE CONJECTURE OF KESKIN, SIAR AND KARAATLI

Rachid Boumahdi, Omar Kihel and Sukrawan Mavecha

Université des Sciences et de la Technologie Houari Boumediène, Laboratoire d'Arithmétique, Codage, Combinatoire et Calcul Formel
1611, El Alia, Alger, Algérie; r_boumehdi 'at' esi.dz

Brock University, Department of Mathematics
Ontario, Canada L2S 3A1; okihel 'at' brocku.ca

King Mongkut's Institute of Technology Ladkrabang, Faculty of Science, Department of Mathematics
Bangkok, 10520, Thailand; sukrawan.ta 'at' kmitl.ac.th

Abstract. In this paper among other results, we will prove the conjecture of Keskin, Siar and Karaatli on the Diophantine equation x² – kxy + y² – 2ⁿ = 0.

2010 Mathematics Subject Classification: Primary 11A07, 11A15, 11D09.

Key words: Diophantine equations, Pell equations, fundamental solution.

Reference to this article: R. Boumahdi, O. Kihel and S. Mavecha: Proof of the conjecture of Keskin, Siar and Karaatli. Ann. Acad. Sci. Fenn. Math. 43 (2018), 557-561.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4328