TY  - JOUR
T1  - On solutions of some Diophantine equations
AU  - Erduvan, Fatih
AU  - Keskin, Refik
AU  - Ged, Kübra
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.35378/gujs.1378010
JF  - Gazi University Journal of Science
PB  - Gazi University
WT  - DergiPark
SN  - 2147-1762
SP  - 891
EP  - 897
VL  - 38
IS  - 2
LA  - en
AB  - Let k and p be prime numbers with p>2. In this note, we find all positive integer solutions to the Diophantine equationsx^2-kxy-y^2=±k, x^2-(k^2+4) y^2=±4k, x^2-2pxy-y^2=±2p, x^2-kxy-y^2=±k(k^2+4) in terms of generalized Fibonacci and Lucas numbers.
KW  - Diophantine equations
KW  - Generalized Fibonacci numbers
KW  - Generalized Lucas numbers
CR  - [1]	Keskin, R., “Solutions of some quadratic Diophantine equations”, Computer and Mathematics with Applications, 60(8): 2225-2230, (2010). DOI: 10.1016/j.camwa.2010.08.012
CR  - [2]	Keskin, R., Güney, Duman, M., “Positive Integer Solutions of Some Pell Equations”, Palestine Journal of Mathematics, 8: 213-226, (2019).
CR  - [3]	Keskin, R., Güney, Duman, M., “Positive Integer Solutions of Some Second-Order Diophantine equations”, Annale Ştiintifice ale Universitatii, “Alexandru Ioan Cuza”, din Iaşi Matematica, (New Series), 3: 649-664, (2017).
CR  - [4]	Ribenboim, P., “My Numbers, My Friends: Popular Lectures on Number Theory”, Springer Verlag, 1-50, (2000).
UR  - https://doi.org/10.35378/gujs.1378010
L1  - https://dergipark.org.tr/en/download/article-file/3483356
ER  -