Prof. Dr. ZAFER ŞİAR

Unvan	PROFESÖR
Birim	FEN-EDEBİYAT FAKÜLTESİ
E-Posta	zsiar@bingol.edu.tr
Dahili No	5734

Öğrenim Bilgisi

DERECE	BÖLÜM/PROGRAM	ÜNİVERSİTE	YIL
Lisans	Matematik	Sakarya Üniversitesi	2005
Yüksek Lisans	Matematik	Sakarya Üniversitesi	2008
Doktor	Matematik	Sakarya Üniversitesi	2012
Doçent	Matematik	Üniversitelerarası Kurum (ÜAK)	2015
Profesör	Matematik	Bingöl Üniversitesi	2021

Akademik Unvanlar

ÜNVAN	ÜNVANIN ALINDIĞI YER	BAŞLAMA TARİHİ	BİTİŞ TARİHİ
Araştırma görevlisi	Bilecik Üniversitesi	20.02.2012	06.12.2013
Yardımcı Doçent	Bingöl Üniversitesi	09.12.2013	20.10.2015
Doçent	Bingöl Üniversitesi	20.10.2015	29.01.2021
Profesör	Bingöl Üniversitesi	29.01.2021

Üniversite Dışı Deneyim

2006-2009 yılları arasında Sınav Dergisi Dershanelerinde Matematik Öğretmenliği

Son Bir Yılda Verilen Dersler

Yıl	Dönem	Dersin Kodu ve Adı	T+U	Öğrenci Sayısı
2016-2017	Güz	İSG118 Matematik	3+0	115
		Mat105 Soyut Matematik I	3+0	2
		Mat1101 Genel Matematik	3+0	91
		Mat2201 Diferansiyel Denklemler	4+0	82
		Mat301 Cebir I	3+1	6
		Mat405 Seminer I	2+0	4
		Mat413 Topolojide Seçme Konular	3+0	7
		Mat1101 Matematik I	4+0	82
2016-2017	Bahar	Mat1102 Matematik II		90
		Lineer Cebir		50
		Olasılık ve İstatistik		83

1) Fatih ERDUVAN, Fibonacci ve Lucas sayılarını içeren bazı üstel Diyofant denklemlerinin çözümleri, Sakarya Üniversitesi, Doktora Tezi, 2021, (Danışman: Prof. Dr. Refik KESKİN, Ortak Danışman: Prof. Dr. Zafer ŞİAR)

2) İbrahim ERDURAN, Logaritmada Lineer Formlar Yardımıyla Bazı Diofant Denklemlerin Çözümü, Bingöl Üniversitesi, Yüksek Lisans Tezi, 2022 (Danışman: Prof. Dr. Zafer ŞİAR)

3) Abdurrahman AKGÜL, Sürekli Kesirler ve Pell Denklemlerine Uygulamaları, Bingöl Üniversitesi, Yüksek Lisans Tezi, 2023 (Danışman: Prof. Dr. Zafer ŞİAR)

4) Ayşe ULÇAN, Altın Oran ve Fibonacci Sayılarının Müzik ile İlişkisi, Bingöl Üniversitesi, Yüksek Lisans Tezi, 2023 (Danışman: Prof. Dr. Zafer ŞİAR)

5) Merve NADİROĞLU, Fibonacci ve Lucas Polinomlarının İntegralleri Üzerine, Bingöl Üniversitesi, Yüksek Lisans Tezi, 2024 (Danışman: Prof. Dr. Zafer ŞİAR)

Yabancı Dil Bilgisi

İngilizce 77.5 (E-YDS) (2015)

Uluslararası Hakemli Dergilerde Yayınlanan Makaleler

1. R. Keskin and Z. Yosma, On Fibonacci and Lucas Numbers of the Form cx² , Journal of Integer Sequences, Vol 14, article 11.9.3 (2011), 1-12. [Full Text online] (PDF)

2. O. Karaatlı and Z. Şiar, On the Diophantine Equation x²- kxy + ky² + ly=0, l ε {1,2,4,8}. Afr. Diaspora J. Math. 14 (2012), no. 1, pp. 24-29.[Full Text online]

3. R. Keskin, O. Karaatlı, and Z. Şiar, On the Diophantine equation x^2 - kxy + y^2 + 2^n = 0, Miskolc Mathematical Notes, Vol 13, 2 (2012), 375-388. [Full Text Online] (PDF)

4. R. Keskin and Z. Şiar, On the Lucas Sequence Equations V_{n}=kV_{m} and U_{n}=kU_{m}, Colloquium Mathematicum, 130 (2013), 27-38.[Full Text Online] (PDF)

5. Z. Şiar and R. Keskin, Some New İdentities Concerning Generalized Fibonacci and Lucas Numbers, Hacettepe Journal of Mathematics and Statistics, 42, 3 (2013), 211-222.[Full Text Online] (PDF)

6. R. Keskin, Z. Şiar and, O. Karaatlı, On the Diophantine equation x^2 - kxy + y^2 -2^n = 0, Czechoslovak Mathematical Journal, 63, 3(2013), 783-797.[Full Text Online] (PDF)

7. R. Keskin, O. Karaatlı, and Z. Şiar, Positive integer solutions of the diophantine equations x^{2} -5F_{n}xy-5(-1)^{n} y^{2}=pm 5^{r}, Miskolc Mathematical Notes, 14, 3(2013), 959-972. [Full Text Online] (PDF)

8. Z. Şiar and R. Keskin, The Square Terms in Generalized Lucas Sequences, Mathematika, 60, 1(2014), 85-100. [Full Text Online] (PDF)

9. R. Keskin and Z. Şiar, Positive Integer Solutions of the Diophantine Equation x²-L_{n}xy+(-1)ⁿy²=±5^{r}, Proceedings - Mathematical Sciences, 124, 3(2014), 301-313. [Full Text Online] (PDF)

10. Z. Şiar, On Square Classes in Generalized Lucas Sequences, International Journal of Number Theory, 11, 2(2015), 661-672. [Full Text Online] (PDF)

11. Z. Şiar and R. Keskin, The Square Terms in Generalized Lucas Sequence with Parameters P and Q, Mathematica Scandinavica, 118 (1) (2016), 13-26. [Full Text Online] (PDF)

12. Z. Şiar and R. Keskin, On Square Classes in Generalized Fibonacci Sequence, Acta Arithmetica, 174 (2016) , 277-295. [Full Text Online] (PDF)

13. R. Keskin, O. Karaatlı, Z. Şiar, and Ü. Öğüt , On the Determination of Solutions of Simultaneous Pell Equations x²-(a²-1)y²=y²-pz²=1, Periodica Mathematica Hungarica 75.2 (2017): 336-344.[Full Text Online]

14. Z. Şiar, Trigonometric Factorizations of the Horadam Sequence and its Companion Sequence, Izvestiya Mathematics, 82(6), (2018), 1265--1277.[Full Text Online]

15. Z. Şiar and R. Keskin, Pythagorean triples containing genaralized Lucas numbers, Turkish Journal of Mathematics, 42, (2018), 1904-1912.[Full Text Online] (PDF)

16. Z. Şiar and R. Keskin, On the Diophantine equation L_n-L_m=3*2^a, Notes on Number Theory and Discrete Mathematics, 24(4), 2018, 112-119.[Full Text Online] (PDF)

17. R. Keskin and Z. Şiar, Some new identities concerning the Horadam sequence and its companion sequence, Communications of the Korean Mathematical Society, 34 (1) (2019), 1-16. [Full Text Online] (PDF)

18. R. Keskin and Z. Şiar, Positive Integer Solutions of Some Diophantine Equations in Terms of Integer Sequences, Afrika Mathematica, 30(1) (2019), 181--194 [Full Text Online] (PDF)

19. Z. Şiar, Lucas Numbers which are products of two Balancing numbers, Notes from International Autumn School on Computational Number Theory, Springer/Birkhäuser's, (2019).[URL]

20. Z. Şiar, F. Erduvan and R. Keskin, Repdigits as products of two Pell or Pell-Lucas Numbers, Acta Math. Univ. Comenianae, 88(2) (2019), 247-256. [Full Text Online] (PDF)

21. R. Keskin, Z. Şiar, M. Güney Duman, and Ü. Öğüt , Solutions of Some Diophantine Equations in Terms of the Horadam Sequence and its Companion Sequence, Tranzactions of A. Razmadze Mathematical Institute, 173 (3) (2019), 79–91.[Full Text Online] (PDF)

22. N. Irmak, Z. Şiar and R. Keskin, On the sum of three arbitrary Fibonacci and Lucas numbers, Notes on Number Theory and Discrete Mathematics, 25(4) (2019), 96--101.[Full Text Online] (PDF)

23. Z. Şiar and R. Keskin, On the Diophantine equation F_n-F_m=2^a, Colloquium Mathematicum, 159 (2020) , 119-126. [Full Text Online] (PDF)

24. Z. Şiar and R. Keskin, Repdigits as sums of two Lucas numbers, Applied Mathematics E-Notes, 20 (2020) , 33--38. [Full Text Online] (PDF)

25. S. G. Rayaguru, G.K. Panda and Z. Şiar, Associated Pell numbers which are repdigits or concatenation of two repdigits, Boletín de la Sociedad Matemática Mexicana, 27(2) (2021), article 54. [Full Text Online ] (PDF )

26. F. Erduvan, R. Keskin and Z. Şiar , Repdigits base b as products of two Pell numbers or Pell-Lucas numbers, Bol. Soc. Mat. Mex., 27(3) (2021), article 70. [Full Text Online ] (PDF )

27. Z. Şiar, R. Keskin and Fatih Erduvan, Fibonacci or Lucas numbers which are products of two repdigits in base b, Bulletin of the Brazilian Mathematical Society, New Series, 52, (2021), 1025–1040.pages1025–1040. [Full Text Online] (PDF)

28. F. Erduvan, R. Keskin, and Z. Şiar, Repdigits base b as products of two Lucas numbers, Quaestiones Mathematicae, 44 (2021), 1283-1293. [Full Text Online] (PDF)

29. F. Erduvan, R. Keskin, and Z. Şiar, Repdigits base b as products of two Fibonacci numbers, The indian journal of pure and applied mathematics, 52 (2021), 861–868. [Full Text Online ] (PDF )

30. Z. Şiar and R. Keskin, On perfect powers which are sum or difference of two Lucas numbers, Miskolc Mathematical Notes, 22 (2) (2021), 951–960. [Full Text Online ] (PDF )

31. Z. Şiar, F. Erduvan, and R. Keskin, Repdigits base b as difference of two Fibonacci numbers, Journal of Mathematical Study, 55(1) (2022), 84-94.[Full Text Online ] (PDF )

32. M.K. Sahukar, Z. Şiar, R. Keskin and G.K. Panda, Perfect powers in sum and difference of two Balancing numbers and its generalization, Notes On Number Theory and Discrete Mathematics, 28(2), 2022, 286--301. [Full Text Online ] (PDF )

33. Z. Şiar and R. Keskin, On the Diophantine equation (a^n-2)(b^n-2)=x^2, Mathematical Notes, 111 (6) 2022, 903–912. [Full Text Online ] (PDF )

34. Z. Şiar and R. Keskin, k-Generalized Pell numbers which are concatenation of two repdigits, Mediterranean Journal of Mathematics, 19(4) 2022, Article 180.[Full Text Online ] (PDF )

35. İ. Erduran and Z. Şiar, All solutions of the Diophantine equation 2F_{n}=3^s.y^b and F_{n}±1=3^s.y^b, Sakarya University Journal of Science 26(3) 2022, 488-492.[Full Text Online ] (PDF )

36. Z. Şiar and R. Keskin, k-generalized Pell numbers which are repdigits in base b, Turkish Journal of Mathematics, 46(8) 2022, 3083-3094. [Full Text Online ] (PDF )

37. Z. Şiar, On the exponential Diophantine equation F_{n}^{x}±F_{m}^{x}=a with a∈{F_{r},L_{r}}, International Journal of Number Theory, 19(1) 2023, 41-57. [Full Text Online ] (PDF )

38. Z. Şiar , R. Keskin, and E. S. Öztaş, On perfect powers in k-Generalized Pell sequence, Mathematica Bohemica 148(4) (2023), 507--518:[Full Text Online ] (PDF )

39. Z. Şiar and R. Keskin, On Perfect Powers in k-Generalized Pell-Lucas numbers, Mathematical Notes, 114(5-6) (2023), 936-948.[Full Text Online ] (PDF )

40. R. Keskin and Z. Şiar, A note on Terai's Conjecture concerning the exponential Diophantine equation x^2+b^y=c^2, (Submitted).

41. R. Keskin, M. Le and Z. Şiar, On the Terai's Conjecture Concerning the Exponential Diophantine Equation x^2 + b^y = c^z (Submitted).

42. Z. Şiar ,Fibonacci or Lucas numbers which are the sumor the di§erence ofsquares of any two Fibonacci numbers Fibonacci and Lucas numbers which are the sum or difference of squares of any two Fibonacci numbers, [Full Text Online ] (PDF )(Preprint).

43. Z. Şiar and R. Keskin, Repdigits in k-Generalized Pell Sequence, https://arxiv.org/pdf/2009.13387.pdf (Preprint).

44. Z. Şiar and İ. Erduran, On the solutions of the Diophantine equation F_{n}±F_{m}=3^s.y^b, the Indian Journal of Pure and Applied Mathematics, (2025) [Full Text Online ] (PDF )

45. Z Şiar, Repdigits base b as products of two k-Generalized Pell numbers, Afrika Matematika, 36,164 (2025) [Full Text Online ] (PDF )

46. Z Şiar, Powers of two as sums of three k-generalized Pell numbers, (Submitted).

47. Z Şiar, F. Luca and F. S. Zottor, Common values of two k-generalized Pell sequences, Notes on Number Theory and Discrete Mathematics, 31(2), (2025), 256–268. [Full Text Online ] (PDF )

48. Z Şiar, Powers of two as sums of two k-generalized Pell-Lucas numbers, (Submitted).

49. Z. Şiar and R. Keskin, The solutions of the Diophantine equation (2^{k}-1)(3^{l}-1)=(7^{m}-1), (Submitted).

50. R. Keskin and Z Şiar, On the Exponential Diophantine Equation (aⁿ-1)(bⁿ-1)=abx², (Accepted).
51. Z Şiar and R. Keskin, The solutions of the Diophantine equation (L_{n}^{k}-1)(L_{n+1}^{l}-1)=L_{n+2}^{m}-1, (Submitted).
52. R. Keskin and Z Şiar, On the Exponential Diophantine Equation (ax^{k}-C)(by^{r}-C)=Dz², (Submitted).

Uluslararası Bilimsel Toplantılarda Sunulan Bildiriler

1. 1^nd International Eurasian Conference on Mathematical Sciences and Applications, Priştine University, KOSOVA (2012), “The Square Terms in Generalized Fibonacci Sequence (Abstract Book)

2. 5th International Eurasian Conference on Mathematical Sciences and Applications, BELGRAD/SIRBİSTAN (2016), (Bildirili) “Trigonometric Factorizations of the Horadam Sequence and its Companion Sequence”.(Abstract Book)

3. International Conference on Mathematics and Mathematics Education (ICMME-2017) Harran University /TURKEY, "Some New Identities Concerning the Horadam Sequence and its Companion Sequence". (Abstract Book)

4. Friendly Workshop On Diophantine Equations And Related Problems (FWDERP-2019) Uludağ University/ TURKEY, "On the exponential Diophantine equation (a^n-2)(b^n-2)=x^2".

5. Webinar on Number Theory and Its Related Topics 2020 (Web-NITRT 2020), Department of Mathematics, Sambalpur University / India, "An Exponential Diophantine Equation Related to the Difference of Powers of Two Fibonacci Numbers".

Ulusal Bilimsel Toplantılarda Sunulan Bildiriler

1. Cebir ve Geometri Günleri, Feza Gürsey Enstitüsü (2010), İSTANBUL, (Bildirili) “Fibonacci and Lucas Numbers of the form cx² ”.(Abstract)

2. 5. Ankara Matematik Günleri, TOBB Üniveristesi (2010)

3. 6. Ankara Matematik Günleri, Hacettepe Üniversitesi (2011), (Bildirili) “ Some New İdentities Concerning Generalized Fibonacci and Lucas Numbers” . (Abstract Book)

4. 9. Ankara Matematik Günleri, Atılım Üniversitesi (2014), (Bildirili) “ Pythagorean triples in Generalized Lucas Sequence”.(Abstract Book)

5. XII. Geometri Sempozyumu, Bilecik Şeyh Edebali Üniversitesi (2014), (Düzenleme Kurulu Üyesi)

6. Bingöl Bilim Sanat Merkezi Üstün Yetenekli Öğrencilere Yönelik Seminer, Bingöl Üniversitesi, “Fibonacci ve Altın Oran” (2015).

Yayın Hakemliği

Mathematical Reviews/MathSciNet Reviewer (Since 2021)

1) Celal Bayar Üniversitesi Fen Bilimleri Dergisi (2016)

2) An International Journal of Optimization and Control: Theories & Applications (IJOCTA) (2017)

3) Ars Combinatoria

4) Honam Journal of Mathematics(2018)

5) Fundamental Journal of Mathematics and Applications (2018)

6) Universal Journal of Mathematics and Applications (2018)

7) Communications in Advanced Mathematical Sciences (2018)

8) The Fibonacci Quarterly (2019)

9) Notes On Number Theory and Discrete Mathematics (2019)

10) Sakarya University Journal of Science (2019)

11) Adıyaman Üniversitesi Fen Bilimleri Dergisi (2020)

12) Iranian Journal of Mathematical Sciences and Informatics (2020)

13) Notes On Number Theory and Discrete Mathematics (2020)

Yazılan Kitaplar ve Kitaplarda Bölümler

Z. Şiar, Lucas Numbers which are products of two Balancing numbers, Notes from International Autumn School on Computational Number Theory, Springer/Birkhäuser's, (2019).[URL]