Yazar "Tekcan, Ahmet" seçeneğine göre listele

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    THE INTEGER SEQUENCE B = B-n(P, Q) WITH PARAMETERS P AND Q
    (Charles Babbage Res Ctr, 2015) Kocapınar, Canan; Özkoç, Arzu; Tekcan, Ahmet
    In 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.
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    On k-balancing numbers
    (Bulgarian Acad Science, 2017) Özkoç, Arzu; Tekcan, Ahmet
    In 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.
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    SOME ALGEBRAIC RELATIONS ON BALANCING NUMBERS
    (Util Math Publ Inc, 2017) Gözeri, Gül Karadeniz; Özkoç, Arzu; Tekcan, Ahmet
    In this work we deduce some new algebraic relations on balancing numbers and their relationships with Pell, Pell-Lucas and oblong numbers. Also we formulate the sums of balancing, Pell and Pell-Lucas numbers in terms of balancing numbers. We deduce some relations on perfect squares, Pythagorean triples, congruent numbers, circulant matrices and spectral norms involving balancing numbers. Later, we formulate the integer solutions of some specific Pell equations via terms of balancing numbers.
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    SOME ALGEBRAIC RELATIONS ON INTEGER SEQUENCES INVOLVING OBLONG AND BALANCING NUMBERS
    (Charles Babbage Res Ctr, 2016) Tekcan, Ahmet; Özkoç, Arzu; Eraşık, Meltem E.
    Let k >= 0 be an integer. Oblong (pronic) numbers are numbers of the form O-k = k(k+1). In this work, we set a new integer sequence B = B-n(k) defined as B-0 = 0, B-1 = 1 and B-n = O-k Bn-1 - Bn-2 for n >= 2 and then derived some algebraic relations on it. Later, we give some new results on balancing numbers via oblong numbers.