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    k-generalized fibonacci numbers close to the form 2a + 3b + 5c
    (Univerzita Komenskeho, 2017) Irmak, N.; Alp, M.
    The k-generalized Fibonacci sequence (formula presented) is defined as the sum of the k proceeding terms and initial conditions are 0,…,0, 1 (k terms). In this paper, we solve the diophantine equation (formula presented), where a, b, c and ? are nonnegative integers with max {a, b} ? c and 0 ? ? ? 5. This work generalizes a recent Marques [9] and the first author, Szalay [6] results. © 2017, Univerzita Komenskeho. All rights reserved.
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    k-GENERALIZED FIBONACCI NUMBERS CLOSE TO THE FORM 2a | 3b | 5c
    (Comenius Univ, 2017) Irmak, N.; Alp, M.
    The k-generalized Fibonacci sequence {F-n((k))}(n >= 0) is defined as the sum of the k proceeding terms and initial conditions are 0, ..., 0, 1 (k terms). In this paper, we solve the diophantine equation F-n((k)) = 2(a) + 3(b) + 5(c) + delta, where a, b, c and delta are nonnegative integers with max {a, b} <= c and 0 <= delta <= 5. This work generalizes a recent Marques [9] and the first author, Szalay [6] results.
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    The order of appearance of the product of two Fibonacci and Lucas numbers
    (Springer, 2020) Irmak, N.; Ray, P. K.
    Let Fn and Ln be the nth Fibonacci and Lucas number, respectively. The order of appearance is defined as the smallest natural number k such that n divides F-k and denoted by z(n) . In this paper, we give explicit formulas for the terms z(FaFb), z(LaLb), z(FaLb) and z(FnFn+pF(n)+2(p)) with p >= 3 prime.
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    TWO-PERIODIC TERNARY RECURRENCES AND THEIR BINET-FORMULA
    (Comenius Univ, 2012) Alp, M.; Irmak, N.; Szalay, L.
    The properties of k-periodic binary recurrences have been discussed by several authors. In this paper, we define the notion of the two-periodic ternary linear recurrence. First we follow Cooper's approach to obtain the corresponding recurrence relation of order six. Then we provide explicit formulae linked to the three possible cases.