Person: TEKCAN, AHMET
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TEKCAN
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AHMET
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Publication Balancing, pell and square triangular functions(Univ Miskolc Inst Math, 2015-01-01) Tekcan, Ahmet; Tayat, Merve; Olajos, Peter; TEKCAN, AHMET; Tayat, Merve; AAH-8518-2021In this work, we derive some functions on balancing, cobalancing, Lucas-balancing, Lucas-cobalancing, Pell, Pell-Lucas and square triangular numbers. At the end of this article we investigated common values of combinatorial numbers and Lucas-balancing numbers.Publication Almost balancing, triangular and square triangular numbers(Bulgarian Acad Science, 2019-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; AAH-8518-2021In this work, we derive some new algebraic relations on all almost balancing numbers (of first and second type) and triangular (and also square triangular) numbers.Publication Quadratic ideals, indefinite quadratic forms and some specific diophantine equations(Soc Paranaense Matematica, 2018-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Kutlu, Seyma; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; AAH-8518-2021Let k >= 1 be an integer and let P = k + 2, Q = k and D = k(2) + 4. In this paper, we derived some algebraic properties of quadratic ideals I-gamma and indefinite quadratic forms F-gamma for quadratic irrationals gamma, and then we determine the set of all integer solutions of the Diophantine equation F-gamma(+/- k) (x, y) = +/- Q.Publication K- Almost balancing numbers(Centre Environment Social & Economic Research Publication-ceser, 2021-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; AAH-8518-2021In this work, we determine the general terms of k-almost balancing numbers and k-almost Lucas-balancing numbers of first and second type in terms of balancing and Lucas-balancing numbers for some integer k >= 1.Publication Positive definite binary quadratic forms and modules over a field(Southeast Asian Mathematical Soc-seams, 2012-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; AAH-8518-2021There has been a connection between binary quadratic forms and modules. Given any quadratic form F, there corresponds a module M-F, and conversely given any module M, there corresponds a binary quadratic form FM. The connection between binary quadratic forms and modules was studied in [3, 4]. In this paper, we consider this connection only for positive definite primitive integral quadratic forms F(x, y) = ax(2)+bxy+cy(2) of discriminant A and modules M over an imaginary quadratic number field F = Q(root Delta).Publication The integer sequence B = Bn(P, Q) with parameters P and Q(Charles Babbage Res Ctr, 2015-07-01) Koçapınar, Canan; Özkoç, Arzu; Tekcan, Ahmet; TEKCAN, AHMET; Uludağ Üniversitesi/Mühendislik Fakültesi/Matematik Bölümü; AAH-8518-2021In this work, we first prove that every prime number p equivalent to 1 (mod 4) can be written of the form P-2-4Q with two positive integers P and Q, and then we define the sequence B-n(P, Q) to be B-0 = 2, B-1 = P and B-n = P Bn-1 - QB(n-2) for n >= 2 and derive some algebraic identities on it. Also we formulate the limit of cross ratio for four consecutive numbers B-n, Bn+1, Bn+2 and Bn+3.Publication On the cycles of indefinite quadratic forms and cycles of ideals II(Southeast Asian Mathematical Soc-seams, 2010-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAH-8518-2021Let P and Q be two positive integers such that P < Q and let D = P-2 + Q(2) be a positive non- square integer. In the first section, we give some preliminaries from binary quadratic forms and quadratic ideals. In the second section, we show that given an ideal I = [Q, P + root D], there exists an indefinite symmetric quadratic form F-I = (Q, 2P,-Q) of discriminant 4 D which corresponds to I. We prove that I is always reduced, and so is F-I. Further, we prove that the cycle of F-I can be obtained using the cycle of I.Publication Almost balancers, almost cobalancers, almost Lucas-balancers and almost lucas-cobalancers(Bulgarian Acad Science, 2023-01-01) Tekcan, Ahmet; Türkmen, Esra Zeynep; TEKCAN, AHMET; Türkmen, Esra Zeynep; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAH-8518-2021; JSX-2084-2023In this work, the general terms of almost balancers, almost cobalancers, almost Lucasbalancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers. Later some relations on all almost balancing numbers and all almost balancers are obtained. Further the general terms of all balancing numbers, Pell numbers and Pell-Lucas number are determined in terms of almost balancers, almost Lucasbalancers, almost cobalancers and almost Lucas-cobalancers of first and second type.Publication On k-balancing numbers(Bulgarian Acad Science, 2017-01-01) Özkoç, Arzu; Tekcan, Ahmet; TEKCAN, AHMET; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAH-8518-2021In this work, we consider some algebraic properties of k-balancing numbers. We deduce some formulas for the greatest common divisor of k-balancing numbers, divisibility properties of k-balancing numbers, sums of k-balancing numbers and simple continued fraction expansion of k-balancing numbers.Publication Representation of integers by hermitian forms(Comenius Univ, 2005-01-01) Tekcan, Ahmet; TEKCAN, AHMET; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAH-8518-2021In this paper we consider the representation of (positive) integers by the Hermitian forms C-n, C-k,C-l and C-k,C-l*.