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Incomplete Fibonacci and Lucas numbers
Rendiconti del Circolo Matematico di Palermo, 1996A particular use of well-known combinatorial expressions for Fibonacci and Lucas numbers gives rise to two interesting classes of integers (namely, the numbersF n(k) andL n(k)) governed by the integral parametersn andk. After establishing the main properties of these numbers and their interrelationship, we study some congruence properties ofL n(k), one
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On Square Pseudo-Lucas Numbers
Canadian Mathematical Bulletin, 1978J. H. E. Cohn (1) has shown thatare the only square Fibonacci numbers in the set of Fibonacci numbers defined byIf n is a positive integer, we shall call the numbers defined by(1)pseudo-Lucas numbers.
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Balancing and Lucas-balancing numbers which are concatenation of three repdigits
Boletín de la Sociedad Matematica Mexicana, 2023S. G. Rayaguru, Jhon J. Bravo
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Lucas's Tests for Mersenne Numbers
The American Mathematical Monthly, 1945(1945). Lucas's Tests for Mersenne Numbers. The American Mathematical Monthly: Vol. 52, No. 4, pp. 188-190.
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On Concatenations of Fibonacci and Lucas Numbers
Bulletin of the Iranian Mathematical Society, 2022M. Alan
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Primitive Divisors of Lucas Numbers
1988Let \( R = \{ {R_n}\} _{n = 1}^\infty \) be a Lucas sequence defined by fixed rational integers A and B and by the recursion relation $$ {R_n} = A \cdot {R_{n - 1}} + B \cdot {R_{n - 2}} $$ for n > 2, where the initial values are R1 = 1 and R2 = A. The terms of R are called Lucas numbers.
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Expansion of Analytic Functions in Terms Involving Lucas Numbers or Similar Number Sequences
, 1965 Paul F. Byrd
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