A note on ratios of Fibonacci hybrid and Lucas hybrid numbers
نویسندگان
چکیده
Irmak recently asked an open question related to divisibility properties of Fibonacci and Lucas quaternions [4, p. 374]. In this paper, we give answer hybrid number version question.
منابع مشابه
Trigonometric Expressions for Fibonacci and Lucas Numbers
The amount of literature bears witness to the ubiquity of the Fibonacci numbers and the Lucas numbers. Not only these numbers are popular in expository literature because of their beautiful properties, but also the fact that they ‘occur in nature’ adds to their fascination. Our purpose is to use a certain polynomial identity to express these numbers in terms of trigonometric functions. It is in...
متن کاملThe Imperfect Fibonacci and Lucas Numbers
A perfect number is any positive integer that is equal to the sum of its proper divisors. Several years ago, F. Luca showed that the Fibonacci and Lucas numbers contain no perfect numbers. In this paper, we alter the argument given by Luca for the nonexistence of both odd perfect Fibonacci and Lucas numbers, by making use of an 1888 result of C. Servais. We also provide a brief historical accou...
متن کاملOn Certain Arithmetic Properties of Fibonacci and Lucas Numbers
mirroring a well-known feature of Fibonacci numbers (see Theorem 2.5). It was pointed out in [1] that (0.2) could itself be used to disprove the corresponding assertion for the 1cm; precisely, if lcm(a, b) = £, then lcm(Ma, Mb) Mt only in the trivial cases a\b or b\a. The argument rested on a uniqueness theorem for the expression of rational numbers as a ratio of two members of the {Mn} sequenc...
متن کاملOn the properties of k-Fibonacci and k-Lucas numbers
In this paper, some properties of k−Fibonacci and k−Lucas numbers are derived and proved by using matrices S = k 2 1 2 k 2+4 2 k 2 and M =
متن کاملOn the intersections of Fibonacci, Pell, and Lucas numbers
We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)} ∞ n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V-sequences when the product of their discriminants is a perfect square. Moreover, the int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notes on Number Theory and Discrete Mathematics
سال: 2021
ISSN: ['1310-5132', '2367-8275']
DOI: https://doi.org/10.7546/nntdm.2021.27.3.73-78