Fibonacci and Lucas numbers of the form $2^{a}+3^{b}+5^{c}$
نویسندگان
چکیده
منابع مشابه
The 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...
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Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...
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In this paper vp(r) denotes the exponent of the highest power of a prime p which divides r and is referred to as the/?-adic order of r. We characterize the/?-adic orders vp(F„) and vp(Ln), i.e., the exponents of a prime/? in the prime power decomposition of Fn and Ln, respectively. The characterization of the divisibility properties of combinatorial quantities has always been a popular area of ...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2013
ISSN: 0386-2194
DOI: 10.3792/pjaa.89.47