منابع مشابه
On the origin of the Fibonacci Sequence
Herein we investigate the historical origins of the Fibonacci numbers. After emphasising the importance of these numbers, we examine a standard conjecture concerning their origin only to demonstrate that it is not supported by historical chronology. Based on more recent findings, we propose instead an alternative conjecture through a close examination of the historical and historical/mathematic...
متن کاملThe Fibonacci Sequence Mod m
We know that ( ) mod n F p forms a periodic sequence (vide Theorem 4). Let ( ) h p denote the length of the sequence. Let p be a prime such that: { } ( ) 2,3 mod 5 p ≡ a sufficient and necessary condition to ensure that ( ) 2 2 h p p + . We shall denote this group 1 G F . Let { } 1, 2 , , k D d d d = be the non-empty set of k divisors of 2 2 p + . Then for ( ) [ ] 1 min G i F h p d = such that ...
متن کاملOn the Entropy of a Two Step Random Fibonacci Substitution
We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a 7→ baa and b 7→ ab, with probability p, and b 7→ ba, with probability 1 − p for 0 < p < 1, and where the random rule is applied each time it acts on a b. We show that the topological entropy of this object is given by the growth rate of the set of inflated ...
متن کاملOn the Periods of the Fibonacci Sequence modulo M
In the last few years I had some occasions to guide activities in a mathematics-with-computer club for 15-year-olds, where we investigated the function K(m) . Theorems 1 and 2 of the present article were found (without proofs) by members of these clubs. To be more specific, these are those of the students results, which I was not able to find in the literature either before or after they have e...
متن کاملOn a Probabilistic Property of the Fibonacci Sequence
Let 77l5..., 77w,... be a sequence of Independent integer-valued random variables. Let SnT]l + -~ + 7jn,Ari = ESn, B* = varS„,P„(m) = P(Sn = m), and f(t,rfj) denote the characteristic function of the random variable 77 •. The local limit theorem (LLT) is formulated as Pn(m) = (27rBy -exp{-(m^f /2B} + o(B~) when n-^00 uniformly for m. The first results on the normal approximation of binomial dis...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2017
ISSN: 1687-1847
DOI: 10.1186/s13662-017-1178-2