## Publications & Works

### SOME ALGEBRAIC RELATIONS ON BALANCING NUMBERS

UTILITAS MATHEMATICA, vol.103, pp.217-236, 2017 (Journal Indexed in SCI)

### TRIANGULAR AND SQUARE TRIANGULAR NUMBERS INVOLVING GENERALIZED PELL NUMBERS

UTILITAS MATHEMATICA, vol.102, pp.231-254, 2017 (Journal Indexed in SCI)

MATHEMATICAL REPORTS, vol.19, no.2, pp.263-279, 2017 (Journal Indexed in SCI)

### SOME ALGEBRAIC RELATIONS ON INTEGER SEQUENCES INVOLVING OBLONG AND BALANCING NUMBERS

ARS COMBINATORIA, vol.128, pp.11-31, 2016 (Journal Indexed in SCI)

### ON ALGEBRAIC IDENTITIES ON A NEW INTEGER SEQUENCE WITH FOUR PARAMETERS

ARS COMBINATORIA, vol.127, pp.225-238, 2016 (Journal Indexed in SCI)

### ON POSITIVE DEFINITE QUADRATIC FORMS AND THE EXTENDED HECKE GROUP (H)over-bar(root 2)

MATHEMATICAL REPORTS, vol.18, no.3, pp.355-361, 2016 (Journal Indexed in SCI)

### THE INTEGER SEQUENCE B = B-n(P, Q) WITH PARAMETERS P AND Q

ARS COMBINATORIA, vol.121, pp.187-200, 2015 (Journal Indexed in SCI)

### BALANCING, PELL AND SQUARE TRIANGULAR FUNCTIONS

MISKOLC MATHEMATICAL NOTES, vol.16, no.2, pp.1219-1231, 2015 (Journal Indexed in SCI)

### THE NUMBER OF SOLUTIONS OF PELL EQUATIONS x(2) - ky(2) = N AND x(2) + xy - ky(2) = N OVER F-p

ARS COMBINATORIA, vol.102, pp.225-236, 2011 (Journal Indexed in SCI)

### Solving some parametric quadratic Diophantine equation over Z and F-p

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.703-706, 2011 (Journal Indexed in SCI)

### n-UNIVERSAL QUADRATIC FORMS, QUADRATIC IDEALS AND ELLIPTIC CURVES OVER FINITE FIELDS

MATHEMATICAL REPORTS, vol.13, no.2, pp.205-216, 2011 (Journal Indexed in SCI)

### Rational Points on Curves over Finite Fields

Ant. Jour. of Mathematics, vol.7, no.4, pp.431-437, 2010 (Journal Indexed in SCI)

### Quadratic Diophantine Equation x(2) - (t(2) - t)y(2) - (4t-2)x + (4t(2)-4t)y=0

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.33, no.2, pp.273-280, 2010 (Journal Indexed in SCI)

### Indefinite Quadratic Forms and their Neighbours

Numerical Analysis and Applied Mathematics, AIP Conf. Proc., vol.1281, pp.1102-1105, 2010 (Journal Indexed in SCI Expanded)

### The Diophantine equation x(2) - (t(2) + t)y(2) - (4t+2)x + (4t(2)+4t)y=0

REVISTA MATEMATICA COMPLUTENSE, vol.23, no.1, pp.251-260, 2010 (Journal Indexed in SCI)

### THE BASE POINTS OF INDEFINITE QUADRATIC FORMS IN THE CYCLE AND PROPER CYCLE OF AN INDEFINITE QUADRATIC FORM

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.36, no.2, pp.101-114, 2007 (Journal Indexed in SCI)

### Proper cycles of indefinite quadratic forms and their right neighbors

APPLICATIONS OF MATHEMATICS, vol.52, no.5, pp.407-415, 2007 (Journal Indexed in SCI)

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.36, no.1, pp.27-36, 2007 (Journal Indexed in SCI)

### Balcobalancing Numbers and Balcobalancers

Creative Mathematics and Informatics, vol.30, no.2, pp.203-222, 2021 (Refereed Journals of Other Institutions)

### k-Almost Balancing Numbers

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, vol.60, no.3, pp.82-89, 2021 (Journal Indexed in ESCI)

### t-cobalancing numbers and t-cobalancers

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, vol.26, no.1, pp.45-58, 2020 (Journal Indexed in ESCI)

### Sums and Spectral Norms of All Almost Balancing Numbers

Creative Mathematics and Informatics, vol.28, no.2, pp.203-214, 2019 (Refereed Journals of Other Institutions)

### Almost balancing, triangular and square triangular numbers

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, vol.25, no.1, pp.108-121, 2019 (Journal Indexed in ESCI)

### Some Algebraic Relations on an Integer Sequence with Fixed Parameter

Acta Universitatis Apulensis, vol.58, pp.53-66, 2019 (Refereed Journals of Other Institutions)

### Base points, bases and positive definite forms

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.11, no.2, 2018 (Journal Indexed in ESCI)

### Finding the Fundamental Solutions of the Pell Equation x{2}-dy{2}= \pm1 by determining the Right Neighbor of F=(d,0,-1)

Libertas Mathematica, vol.38, no.1, pp.1-13, 2018 (Refereed Journals of Other Institutions)

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, vol.36, no.3, pp.173-192, 2018 (Journal Indexed in ESCI)

### t-Balancing Numbers, Pell Numbers and Square Triangular Numbers. 33(2017), 133-146

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, vol.33, pp.133-146, 2017 (Refereed Journals of Other Institutions)

### The Integer Sequence a_{n} and its Relationship with Pell, Pell-Lucas and Balancing Numbers

Annales Univ. Sci. Budapest., Sect. Comp, vol.46, pp.275-288, 2017 (Refereed Journals of Other Institutions)

### The Pell Equation x {2}-(k {2}-2)y {2}=1 and the Corresponding Integer Sequence

Annales Univ. Sci. Budapest., Sect. Comp., vol.46, pp.303-325, 2017 (Refereed Journals of Other Institutions)

### On k-balancing numbers

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, vol.23, no.3, pp.38-52, 2017 (Journal Indexed in ESCI)

### Letter to the Editor: Disproof the Conjecture Related to the Pell Equation x{2}-D y{2}=2 by Özen Özer

Adv. in Theor. and App. Maths., vol.9, no.1, pp.49-59, 2014 (Refereed Journals of Other Institutions)

### Generalized Pell Numbers Balancing Numbers and Binary Quadratic Forms

Creative Mathematics and Informatics, vol.23, no.1, pp.115-122, 2014 (Refereed Journals of Other Institutions)

### The Diophantine Equation 8x^{2}-y^{2}+8x(1+t)+(2t+1)^{2} and t-Balancing Numbers

ISR Combinatorics, vol.897834, pp.1-5, 2014 (Refereed Journals of Other Institutions)

### Sequences of Right and Left Neighbors of Six Type Indefinite Binary Quadratic Forms and their Proper Automorphisms

Jour. of Maths. Sci.: Adv. App, vol.20, pp.1-19, 2013 (Refereed Journals of Other Institutions)

### Pell Form and Pell Equation via Oblong Numbers

Serdica Math. Jour., vol.39, pp.37-52, 2013 (Refereed Journals of Other Institutions)

### Positive Definite Binary Quadratic Forms and Modules over a Field

Southeast Asian Bulletin of Mathematics, vol.36, pp.419-426, 2012 (Refereed Journals of Other Institutions)

### On Kaprekar Numbers

Advances in Theoretical and App. Maths., vol.7, no.1, pp.43-50, 2012 (Refereed Journals of Other Institutions)

### Some Algebraic Identities on the Integer Sequence Associated with Imaginary Quadratic Number Field \mathbb{Q}(\sqrt{-163})

Selçuk Journal of Applied Mathematics, vol.12, no.1, pp.149-160, 2011 (Refereed Journals of Other Institutions)

### Representations of Positive Integers by Positive Quadratic Forms

Southeast Asian Bulletin of Mathematics, vol.35, no.1, pp.137-148, 2011 (Journal Indexed in ESCI)

### Principal Indefinite Quadratic Forms and Singular Curves over Finite Fields

Southeast Asian Bulletin of Mathematics, vol.35, no.5, pp.859-867, 2011 (Refereed Journals of Other Institutions)

### Continued Fraction Expansion of \sqrt{D} and Pell Equation x^{2}-Dy^{2}=1

Mathematica Moravica, vol.15, no.2, pp.19-27, 2011 (Refereed Journals of Other Institutions)

### Neighbors of Indefinite Binary Quadratic Forms

I.J.of Comp.and M.Sci, vol.5, no.1, pp.16-22, 2011 (Refereed Journals of Other Institutions)

### Quadratic Forms Elliptic Curves and Integer Sequence

Acta Universitatis Apulensis, vol.25, pp.9-30, 2011 (Refereed Journals of Other Institutions)

Bulletin of Irish Math. Society, vol.65, pp.11-21, 2010 (Refereed Journals of Other Institutions)

### Elliptic Divisibility Sequences over Finite Fields

Int. Journal of Comp. and Math.Sci., vol.4, no.1, pp.12-19, 2010 (Refereed Journals of Other Institutions)

### The Diophantine Equation x^{2}-Py^{2}=Q

Int. Jour. of Comp. and Math.Sci., vol.4, no.2, pp.59-62, 2010 (Refereed Journals of Other Institutions)

### The Cubic Congruence x^{3}+ax^{2}+bx+c \equiv 0 (\mod p) and Binary Quadratic Forms F(x,y)=ax^{2}+bxy+cy^{2} II

Acta Universitatis Apulensis, vol.22, pp.53-63, 2010 (Refereed Journals of Other Institutions)

### On Cycles and Products of Ideals and Corresponding Indefinite Quadratic Forms

Comptes rendus mathématiques-Math. Reports, vol.32, no.2, pp.40-51, 2010 (Refereed Journals of Other Institutions)

### Positive Definite Quadratic Forms Elliptic Curves and Cubic Congruences

Inter. Jour. of Comp. and Math.Sci, vol.4, no.2, pp.100-104, 2010 (Refereed Journals of Other Institutions)

### On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals II

Southeast Asian Bulletin of Mathematics, vol.34, pp.185-192, 2010 (Refereed Journals of Other Institutions)

### The Family of Indefinite Binary Quadratic Forms and Elliptic Curves over Finite Fields

General Mathematics, vol.18, no.4, pp.3-17, 2010 (Refereed Journals of Other Institutions)

### The Elliptic Curves y^{2}=x^{3}-1728x over Finite Fields

Journal of Algebra, Number Theory: Advances and Applications, vol.1, no.1, pp.61-74, 2009 (Refereed Journals of Other Institutions)

### The Number of Rational Points on Singular Curves y{2}=x(x-a){2} over Finite Fields \mathbb{F}_{p}.

Int. Journal of Comp.and Math.Sci., vol.3, no.1, pp.14-17, 2009 (Refereed Journals of Other Institutions)

Comptes rendus mathématiques-Mathematical Reports, vol.31, no.2, pp.53-64, 2009 (Refereed Journals of Other Institutions)

Int. Jour. of Comp.and Math. Sci., vol.3, no.2, pp.56-59, 2009 (Refereed Journals of Other Institutions)

### Representation of Integers by Quadratic Forms in Several Variables

Creative Maths. and Infor., vol.18, no.1, pp.65-75, 2009 (Refereed Journals of Other Institutions)

### The Diophantine Equation y^{2}-2yx-3=0 and Corresponding Curves over \mathbb{F}_{p}

Int. Journal of Comp.and Math.Sci, vol.3, no.6, pp.260-263, 2009 (Refereed Journals of Other Institutions)

### A.Tekcan. The Pell Equation x{2}-(k{2}-k)y{2}=2{t}.

Int. Jour. of Comp. and Math. Sci, vol.2, no.1, pp.5-9, 2008 (Refereed Journals of Other Institutions)

### Some Relations Involving the Sums of Fibonacci Numbers

Proceedings of the Jangjeon Math. Soc., vol.11, no.1, pp.1-12, 2008 (Refereed Journals of Other Institutions)

### The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

Int. Journal of Comp.and Math.Sci, vol.2, no.2, pp.58-63, 2008 (Refereed Journals of Other Institutions)

### Elliptic Curves Conics and Cubic Congruences Associated with Indefinite Binary Quadratic Forms

Novi Sad J. Math., vol.38, no.2, pp.71-81, 2008 (Refereed Journals of Other Institutions)

### The Pell Equation x^{2}+xy-ky^{2}=\pm1

Global Journal of Pure and Applied Maths., vol.4, no.2, pp.105-112, 2008 (Refereed Journals of Other Institutions)

Novi Sad Journal of Maths., vol.38, no.1, pp.83-96, 2008 (Refereed Journals of Other Institutions)

### On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals III

Comptes rendus mathématiques-Mathematical Reports, vol.30, no.1, pp.22-32, 2008 (Refereed Journals of Other Institutions)

### The Number of Rational Points on Elliptic Curves y^{2}= x^{3}+b^{2} over Finite Fields

Int. Jour. of Comp. and Math. Sci., vol.1, no.3, pp.178-184, 2007 (Refereed Journals of Other Institutions)

### The Elliptic Curves y^{2}=x^{3}-t^{2}x over \mathbb{F}_{p}

Int. J.of Comp.and Math.Sci, vol.1, no.3, pp.165-171, 2007 (Refereed Journals of Other Institutions)

### On the Pell Equation x^{2}-(k^{2}-2)y^{2}=2^{t}

Crux Mat. with Math.May., vol.33, no.6, pp.361-365, 2007 (Refereed Journals of Other Institutions)

### The Number of Rational Points on Conics C_{p,k}:x^{2}-ky^{2}=1 over Finite Fields \mathbb{F}_{p}

International Journal of Computational and Mathematical Sciences, vol.1, no.2, pp.150-153, 2007 (Refereed Journals of Other Institutions)

### The Pell Equation x^{2}-Dy^{2}=\pm 4

Applied Math. Science, vol.1, no.8, pp.363-369, 2007 (Refereed Journals of Other Institutions)

### On Indefinite Binary Quadratic Forms Cubic Congruence and Elliptic Curves

Inter. Jour. of Cont. Math. Science, vol.2, no.21, pp.1031-1037, 2007 (Refereed Journals of Other Institutions)

### Some Relations on Lucas Numbers and their Sums

Advanced Studies in Contemporary Mathematics, vol.15, no.2, pp.195-211, 2007 (Refereed Journals of Other Institutions)

### Representations of Positive Integers by Positive Quadratic Forms and the Fourier Coefficients of Cusp Forms

Southeast Asian Bull. of Maths, vol.31, pp.349-362, 2007 (Refereed Journals of Other Institutions)

### Some Algebraic Properties of Universal and Regular Covering Spaces

International Journal of Comp. and Mathematics Sciences, vol.1, no.4, pp.251-254, 2007 (Refereed Journals of Other Institutions)

### A Second Approach to the Proper Cycles of Indefinite Quadratic Forms and their Right Neighbors

International Journal of Contemporary Math. Sci, vol.2, no.6, pp.249-260, 2007 (Refereed Journals of Other Institutions)

### On the Integer Solutions of the Pell Equation x^{2}-dy^{2}=2^{t}

Int. Jour. of Comp. and Math, vol.1, no.3, pp.204-208, 2007 (Refereed Journals of Other Institutions)

### Solving the Pell Equation using the Fundamental Element of the Field \mathbb{Q}(\sqrt{\Delta })

Southeast Asian Bull. of Maths., vol.30, pp.355-366, 2006 (Refereed Journals of Other Institutions)

### Signatures of the Special Congruence Subgroup of the Extended Modular Group

Southeast Asian Bull. of Maths., vol.30, pp.1147-1156, 2006 (Refereed Journals of Other Institutions)

### The Number of Representations of Positive Integers by Positive Quadratic Forms

Proceedings of the Jangjeon Math. Soc., vol.9, no.2, pp.125-136, 2006 (Refereed Journals of Other Institutions)

### Cycles of Indefinite Quadratic Forms and Cycles of Ideals

Hacettepe Journal of Maths. and Sta., vol.35, no.1, pp.63-70, 2006 (Refereed Journals of Other Institutions)

Bulletin of the Irish Mathematical Society, vol.58, pp.69-79, 2006 (Refereed Journals of Other Institutions)

### Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms

Turkish Journal of Mathematics, vol.29, pp.141-156, 2005 (Refereed Journals of Other Institutions)

### Representation of Integers by Hermitian Forms

Acta Mathematica Universitatis Comenianae, vol.74, no.2, pp.205-209, 2005 (Refereed Journals of Other Institutions)

### Representations of Positive Integers by a Direct Sum of Quadratic Forms

Results in Mathematics, vol.46, pp.146-163, 2004 (Refereed Journals of Other Institutions)

### On the Number of Representations of Positive Integers by Quadratic Forms as the Basis of the Space S_{4}(\Gamma_{0}(47),1)

Int. Jour. of Math. and Math. Sci, vol.2014, no.12, pp.637-646, 2004 (Refereed Journals of Other Institutions)

### On the Representation of Positive Integers by Quadratic Forms with Seven Variables

Southeast Asian Bull. of Maths., vol.28, no.5, pp.875-886, 2004 (Refereed Journals of Other Institutions)

### Pell Equation x^{2}-Dy^{2}=2, II

Bulletin of Irish Math. Society, vol.54, pp.73-89, 2004 (Refereed Journals of Other Institutions)

### The Connection between Quadratic Forms and the Extended Modular Group

Mathematica Bohemica, vol.128, no.3, pp.225-236, 2003 (Refereed Journals of Other Institutions)

### On the Covering Space and the Automorphism Group of the Covering Space

Balkan Journal of Geometry and Its App, vol.8, no.1, pp.101-108, 2003 (Refereed Journals of Other Institutions)

### Some Relations via k Balancing Numbers

4th Int. Eurasian Conference on Mathematical Sciences and App. (IECMSA-20015), Atina, Greece, 31 August - 03 September 2015, vol.1, pp.29

### Triangular and Square Triangular Numbers

Numerical Computations: Theory and Algorithms NUMTA2013, Flerna, Italy, 17 - 23 June 2013, pp.5

### Some Properties of Universal Binary Quadratic Forms

The 24th International Conference of Jangjeon Mathematical Society, Konya, Turkey, 20 - 23 July 2011, pp.38

### Integer Solutions of a Special Diophantine Equation

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Greece, 19 - 25 September 2011, vol.1389

### On the Integer Solutions of Diophantine Equation

Int. Congress in Honour of Professor H.M.Srivastava on his 70th Birth Anniversary, Bursa, Turkey, 18 - 21 August 2010, pp.98

### P ve Q parametreli C=C_{n} Tamsayı Dizisi Üzerinde Bazı Cebirsel Özdeşlikler

XXIII. Ulusal Matematik Sempozyumu, Kayseri, Turkey, 4 - 07 August 2010, pp.71

### x^{2}-(t^{2}-t)y^{2}-(4t-2)x+(4t^{2}-4t)y=0 Diophantine Denklemi

5. Ankara Matematik Günleri, Ankara, Turkey, 3 - 04 June 2010, pp.12

### Indefinite Kuadratik Formların Denklikleri Taban Noktaları ve Komşuları

5. Ankara Matematik Günleri, Ankara, Turkey, 3 - 04 June 2010, pp.8

### Primes in Z[exp(2 pi i/3)]

International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 19 - 25 September 2010, vol.1281, pp.1129-1130

### Indefinite Quadratic Forms and their Neighbours

International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 19 - 25 September 2010, vol.1281, pp.1102-1105

### Indefinite Kuadratik Formlar Eliptik Eğriler ve Kübik Kongrüanslar

XXII. Ulusal Matematik Sempozyumu, İzmir, Turkey, 31 August - 03 September 2009, pp.64

### İndefinite Kuadratik Formların Sağ ve Sol Komşuları

XXII. Ulusal Matematik Sempozyumu, İzmir, Turkey, 31 August - 03 September 2009, pp.70

### The Relationship among Elliptic Divisibility Sequences Elliptic Curves and Binary Quadratic Forms

Antalya Algebra Days X, Antalya, Turkey, 28 May - 01 June 2008, pp.45

### The Number of Rational Points on Elliptic Curves Related to Binary Quadratic Forms

Antalya Algebra Days X, Antalya, Turkey, 28 May - 01 June 2008, pp.38-39

### On the Elliptic Divisibility Sequences over Finite Fields

5-th Europan Congress of Mathematics, Amsterdam, Netherlands, 14 - 18 July 2008, pp.85

### Right Neighbors and Base Points of Indefinite Binary Quadratic Forms

Workshop on Mathematical Methods in Applied Science, Bursa, Turkey, 22 - 23 May 2008, pp.38

### Some Properties of Elliptic Divisibility Sequences over Finite Fields

Workshop on Mathematical Methods in Applied Science, Bursa, Turkey, 22 - 23 May 2008, pp.36

### On the Singular Elliptic Curves over Finite Fields

Antalya Algebra Days IX, Antalya, Turkey, 22 - 27 May 2007, pp.61

### The Connection between Principal Indefinite Quadratic Forms and Elliptic Curves

Antalya Algebra Days-IX, Antalya, Turkey, 22 - 27 May 2007, pp.66

### Sonlu Cisimler Üzerinde Tanımlı y^{2}=x^{3}+b^{2} Eliptik Eğrileri Üzerindeki Rasyonel Noktaların Sayısı

XIX. Ulusal Matematik Sempozyumu, Kütahya, Turkey, 22 - 25 August 2006, pp.44

### Sonlu Cisimler Üzerinde Tanımlı Frey Eliptik Eğrileri Üzerindeki Rasyonel Noktalar

XIX. Ulusal Matematik Sempozyumu, Kütahya, Turkey, 22 - 25 August 2006, pp.43

XIX. Ulusal Matematik Sempozyumu, Kütahya, Turkey, 22 - 25 August 2006, pp.42

### Pozitif Tanımlı Kuadratik Formların Taban Noktaları

XVIII. Ulusal Matematik Sempozyumu, İstanbul, Turkey, 5 - 08 September 2005, pp.68

XVII. Ulusal Matematik Sempozyumu, Bolu, Turkey, 23 - 26 August 2004, pp.89-101

### İleri Analiz

Dora Yayıncılık, 2020

### Genel Matematik I

Dora, Bursa, 2010

### Genel Matematik II

Dora, Bursa, 2009