FIBONACCI NUMBERS MODULO CUBES OF PRIMES
نویسندگان
چکیده
منابع مشابه
Fibonacci Numbers modulo Cubes of Primes
Let p be an odd prime. It is well known that Fp−( p 5 ) ≡ 0 (mod p), where {Fn}n>0 is the Fibonacci sequence and (−) is the Jacobi symbol. In this paper we show that if p 6= 5 then we may determine Fp−( p 5 ) mod p3 in the following way:
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For any modulus m ≥ 2 and residue b (mod m) (we always assume 1 ≤ b ≤ m), denote by ν(m, b) the frequency of b as a residue in one period of the sequence {Fn (mod m)}. It was proved that ν(5k, b) = 4 for each b (mod 5k) and each k ≥ 1 by Niederreiter in 1972 [7]. Jacobson determined ν(2k, b) for k ≥ 1 and ν(2k5j , b) for k ≥ 5 and j ≥ 0 in 1992 [6]. Some other results in this area can be found ...
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Let F0 = 0, F1 = 1, and Fn = Fn−1 + Fn−2 for n ≥ 2 denote the sequence F of Fibonacci numbers. For any modulus m ≥ 2 and residue b (modm), denote by vF (m, b) the number of occurrences of b as a residue in one (shortest) period of F modulo m. Moreover, let vL(m, b) be similarly defined for the Lucas sequence L satisfying L0 = 2, L1 = 1, and Ln = Ln−1 + Ln−2 for n ≥ 2. In this paper, completing ...
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A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...
متن کاملIndependent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes
A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2013
ISSN: 1027-5487
DOI: 10.11650/tjm.17.2013.2488