منابع مشابه
Aliquot sums of Fibonacci numbers
Here, we investigate the Fibonacci numbers whose sum of aliquot divisors is also a Fibonacci number (the prime Fibonacci numbers have this property).
متن کاملDistribution of the Fibonacci numbers modulo 3
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 ...
متن کاملFibonacci 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:
متن کاملRepdigits as sums of three Fibonacci numbers
In this paper, we find all base 10 repdigits which are sums of three Fibonacci numbers. AMS subject classifications: Primary 11D61; Secondary 11A67, 11B39
متن کاملAlternating sums of reciprocal generalized Fibonacci numbers
ABSTRACT Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2010
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972710001693