Karaatli, Olcay; Keskin, Refik On the Lucas sequence equations \(V_n=7\,\square \) and \(V_n=7V_m\,\square \). (English) Zbl 1387.11014 Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 335-353 (2018). MSC: 11B39 11D09 PDFBibTeX XMLCite \textit{O. Karaatli} and \textit{R. Keskin}, Bull. Malays. Math. Sci. Soc. (2) 41, No. 1, 335--353 (2018; Zbl 1387.11014) Full Text: DOI
Keskin, Refik; Karaatli, Olcay; Şiar, Zafer; Öğut, Ümmügülsüm On the determination of solutions of simultaneous Pell equations \(x^2 - (a^2 - 1) y^2 = y^2 - pz^2 = 1\). (English) Zbl 1413.11064 Period. Math. Hung. 75, No. 2, 336-344 (2017). MSC: 11D25 11B37 11B39 PDFBibTeX XMLCite \textit{R. Keskin} et al., Period. Math. Hung. 75, No. 2, 336--344 (2017; Zbl 1413.11064) Full Text: DOI
Karaatlı, Olcay On the {L}ucas sequence equations {\(V_n(P,1)=wkx^2\)}, {\(w\in\{5,7\}\)}. (English) Zbl 1389.11037 Period. Math. Hung. 73, No. 1, 73-82 (2016). Reviewer: Florian Luca (Morelia) MSC: 11B37 11B39 11B50 PDFBibTeX XMLCite \textit{O. Karaatlı}, Period. Math. Hung. 73, No. 1, 73--82 (2016; Zbl 1389.11037) Full Text: DOI
Karaatli, Olcay On generalized Fibonacci and Lucas numbers of the form \(wkx^{2} \pm 1\). (English) Zbl 1351.11010 Integers 16, Paper A26, 12 p. (2016). MSC: 11B39 PDFBibTeX XMLCite \textit{O. Karaatli}, Integers 16, Paper A26, 12 p. (2016; Zbl 1351.11010) Full Text: EMIS
Karaatlı, Olcay; Keskin, Refik On the equations \(U_{n}=5\square\) and \(V_{n}=5\square\). (English) Zbl 1349.11027 Miskolc Math. Notes 16, No. 2, 925-938 (2016). MSC: 11B39 11D09 PDFBibTeX XMLCite \textit{O. Karaatlı} and \textit{R. Keskin}, Miskolc Math. Notes 16, No. 2, 925--938 (2016; Zbl 1349.11027) Full Text: DOI
Karaatlı, Olcay The terms of the form \(7kx^{2}\) in the generalized Lucas sequence with parameters \(P\) and \(Q\). (English) Zbl 1359.11020 Acta Arith. 173, No. 1, 81-95 (2016). Reviewer: Thomas Stoll (Vandœuvre-lés Nancy) MSC: 11B39 11B37 11B50 PDFBibTeX XMLCite \textit{O. Karaatlı}, Acta Arith. 173, No. 1, 81--95 (2016; Zbl 1359.11020) Full Text: DOI
Karaatli, Olcay; Keskin, Refik Generalized Lucas numbers of the form \(5kx^2\) and \(7kx^2\). (English) Zbl 1395.11032 Bull. Korean Math. Soc. 52, No. 5, 1467-1480 (2015). MSC: 11B39 11B50 PDFBibTeX XMLCite \textit{O. Karaatli} and \textit{R. Keskin}, Bull. Korean Math. Soc. 52, No. 5, 1467--1480 (2015; Zbl 1395.11032) Full Text: DOI
Keskin, Refik; Karaatli, Olcay Generalized Fibonacci and Lucas numbers of the form \(5x^2\). (English) Zbl 1379.11015 Int. J. Number Theory 11, No. 3, 931-944 (2015). MSC: 11B39 11A07 PDFBibTeX XMLCite \textit{R. Keskin} and \textit{O. Karaatli}, Int. J. Number Theory 11, No. 3, 931--944 (2015; Zbl 1379.11015) Full Text: DOI arXiv
Karaatli, Olcay; Keskín, Refík; Zhu, Huilin Infinitely many positive integer solutions of the quadratic Diophantine equation \(x^2-8B_nxy-2y^2=\pm 2^r\). (English) Zbl 1309.11024 Ir. Math. Soc. Bull. 73, 29-45 (2014). MSC: 11D09 11B39 PDFBibTeX XMLCite \textit{O. Karaatli} et al., Ir. Math. Soc. Bull. 73, 29--45 (2014; Zbl 1309.11024) Full Text: Link
Keskin, Refik; Karaatlı, Olcay; Ṣiar, Zafer Positive integer solutions of the Diophantine equations \(x^2 -5 F_n xy -5(-1)^n y^2=\pm 5^r\). (English) Zbl 1286.11028 Miskolc Math. Notes 14, No. 3, 959-972 (2013). MSC: 11D09 11B37 11B39 PDFBibTeX XMLCite \textit{R. Keskin} et al., Miskolc Math. Notes 14, No. 3, 959--972 (2013; Zbl 1286.11028)
Keskin, Refik; Ṣiar, Zafer; Karaatlı, Olcay On the Diophantine equation \(x^2-kxy+y^2-2^n=0\). (English) Zbl 1290.11060 Czech. Math. J. 63, No. 3, 783-797 (2013). Reviewer: Thomas Stoll (Vandœuvre-lés Nancy) MSC: 11D09 11D45 11B39 PDFBibTeX XMLCite \textit{R. Keskin} et al., Czech. Math. J. 63, No. 3, 783--797 (2013; Zbl 1290.11060) Full Text: DOI
Karaatlı, Olcay; Keskin, Refik Integral points on the elliptic curve \(y^2=x^3+27x-62\). (English) Zbl 1290.11063 J. Inequal. Appl. 2013, Paper No. 221, 6 p. (2013). MSC: 11D25 11B39 PDFBibTeX XMLCite \textit{O. Karaatlı} and \textit{R. Keskin}, J. Inequal. Appl. 2013, Paper No. 221, 6 p. (2013; Zbl 1290.11063) Full Text: DOI
Keskin, Refik; Karaatlı, Olcay Some new properties of balancing numbers and square triangular numbers. (English) Zbl 1291.11030 J. Integer Seq. 15, No. 1, Article 12.1.4, 13 p. (2012). MSC: 11B37 11A07 11B39 11D09 11D72 PDFBibTeX XMLCite \textit{R. Keskin} and \textit{O. Karaatlı}, J. Integer Seq. 15, No. 1, Article 12.1.4, 13 p. (2012; Zbl 1291.11030) Full Text: EMIS
Karaatlı, Olcay; Ṣiar, Zafer On the Diophantine equation \(x^2-kxy+ky^2+ly=0\), \(l\in\{1,2,4,8\}\). (English) Zbl 1290.11059 Afr. Diaspora J. Math. 14, No. 1, 24-29 (2012). MSC: 11D09 11B37 11B39 PDFBibTeX XMLCite \textit{O. Karaatlı} and \textit{Z. Ṣiar}, Afr. Diaspora J. Math. 14, No. 1, 24--29 (2012; Zbl 1290.11059) Full Text: Euclid
Keskin, Refik; Karaatli, Olcay; Ṣiar, Zafer On the Diophantine equation \(x^2-kxy + y^2 +2^n = 0\). (English) Zbl 1274.11079 Miskolc Math. Notes 13, No. 2, 375-388 (2012). MSC: 11D09 11B37 11B39 PDFBibTeX XMLCite \textit{R. Keskin} et al., Miskolc Math. Notes 13, No. 2, 375--388 (2012; Zbl 1274.11079)