Results 1  10
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155
σk(Fm) = Fn
, 2010
"... Let σk(n) be the sum of the kth powers of the divisors of n. Here, we prove that if (Fn)n≥1 is the Fibonacci sequence, then the only solutions of the equation σk(Fm) = Fn in positive integers k ≥ 2, m and n have k = 2 and m ∈ {1, 2, 3}. The proof uses linear forms in two and three logarithms, latti ..."
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Let σk(n) be the sum of the kth powers of the divisors of n. Here, we prove that if (Fn)n≥1 is the Fibonacci sequence, then the only solutions of the equation σk(Fm) = Fn in positive integers k ≥ 2, m and n have k = 2 and m ∈ {1, 2, 3}. The proof uses linear forms in two and three logarithms
Some Remarks On the Equation Fn = kFm In Fibonacci Numbers
"... Let {Fn} ∞ n=1 = {1, 1, 2, 3,...} be the sequence of Fibonacci numbers. In this paper we give some sufficient conditions on a natural number k such that the equation Fn = kFm is solvable with respect to the unknowns n and m. We also show that for k> 1 the equation Fn = kFm has at most one soluti ..."
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Let {Fn} ∞ n=1 = {1, 1, 2, 3,...} be the sequence of Fibonacci numbers. In this paper we give some sufficient conditions on a natural number k such that the equation Fn = kFm is solvable with respect to the unknowns n and m. We also show that for k> 1 the equation Fn = kFm has at most one
Representing FM in Isabelle
, 1994
"... this report research is done in representing a database specification language in the proof system Isabelle. This representation must become the base for a tool for the verification of database specifications. We use FM (which stands for Formal Model) as our database specification language. FM has p ..."
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this report research is done in representing a database specification language in the proof system Isabelle. This representation must become the base for a tool for the verification of database specifications. We use FM (which stands for Formal Model) as our database specification language. FM has
ON THE OCCURRENCE OF Fn IN THE ZECKENDORF DECOMPOSITION OF nFn
, 1997
"... The Zeckendorf decomposition of a natural number n is the unique expression of n as a sum of Fibonacci numbers with nonconsecutive indices and with each index greater than 1, where FQ = 0, Fx = l, and FM Fi + Fi_l form the Fibonacci numbers for i> 0 (see [6] and [8], or see pages 10809 in [7]). ..."
Abstract

Cited by 1 (1 self)
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The Zeckendorf decomposition of a natural number n is the unique expression of n as a sum of Fibonacci numbers with nonconsecutive indices and with each index greater than 1, where FQ = 0, Fx = l, and FM Fi + Fi_l form the Fibonacci numbers for i> 0 (see [6] and [8], or see pages 10809 in [7
(Fm1 + Fm+i)< Lemma. For 1 < r <m let Gr Fm„f + Fm+i Fr. Then
"... In the work of Wall [2], a function £ was defined by "<j>fm) is the length of the period of the sequence of Fibonacci numbers reduced to least nonnegative residues modulo m, for m> 2. " Thus, the domain of <£is the set of positive integers greater than 2, and the range vvas sh ..."
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shown to be a subset of the set of all even integers. Below, I determine the range of £ exactly. In [1] I proved the following Theorem A. If m is an integer greater than 3 then $fFm)2m if m is even and <j>(Fm) 4m if m is odd. Here, Fm is the m th Fibonacci number, where F0 = 0, Fx = 7, Fn+g * Fn
THE WAVELENGTHRATIO METHOD: A NOVEL APPROACH TO EXTINCTIONFREE DETERMINATION OF FM/FN
"... Résumé. Les variations, en fonction de la longueur d'onde, des réflectivités p+ et p _ correspondant aux deux polarisations des neutrons incidents devraient, pour un monocristal magnétique en forme de plaque, être liées par une loi d'échelle indépendante de l'extinction. Cette propr ..."
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Résumé. Les variations, en fonction de la longueur d'onde, des réflectivités p+ et p _ correspondant aux deux polarisations des neutrons incidents devraient, pour un monocristal magnétique en forme de plaque, être liées par une loi d'échelle indépendante de l'extinction. Cette propriété permettrait, moyennant vérification expérimentale, d'obtenir très directement le rapport des composantes magnétiques et nucléaires des facteurs de structure, sans avoir à effectuer des corrections d'extinction. Abstract. The variations with wavelength of the reflectivities p+ and p _ corresponding to the two polarization states of the incident neutrons should be related through an extinction independent scaling law in the case of a plateshaped crystal. If borne out by experiment, this property should provide a very direct way of measuring the ratio of the magnetic and nuclear contributions to the structure factor, without use of extinction corrections. 1.
P0341 (Proceeding for EPTC2007).fm
"... Abstract Strong crescent bond and strong tail bond are crucial for maintaining reliability and bondability of the wire bond and stability of the bonding process, respectively. This study investigates the optimization of tail breaking force and pull force of the crescent bonding process with insulat ..."
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with insulated XWire TM . The pull force and the tail breaking force are individually optimized by an iteration method. The results are compared with the results of bare Au wire. Ultrasonic power which is a measure of ultrasonic amplitude, combined with a cleaning stage during bonding plays a significant role
Packet Classification Using Multidimensional Cutting
 In Proceedings of ACM SIGCOMM
, 2003
"... cTd[e<fhgWigj k eZl.m&kIn;oGpWqVjVfiEqVrZif&f&etsuqViMmIe<nlviMrZwnkIetmIdWxyqVir<r<jzo{~} A "'MOQ;`1I^Se<jFmIdWjFg[kIj Ge<npWf&rt3jVf_m;lWnz>liMrZwnkIetmIdWx rZwnkIetmIdW %Ggj k"^p[mIfEe<f 310 m;lWnz>liM eZf&e<nlm&kIjVjf_m& ..."
Abstract

Cited by 152 (8 self)
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VrZiMf&f&e<sWqziMmIe<nlir<wnkIetmIdWxfVGgj k"^pGmIfp[f&jVf8mInV mIe<xjVfrZj f&fOxjVxnk&mIduilh~eb^pGmIfngGmIeZxe<VjVoYnkxjVxnMk&.V>dWe<r<j mId[jFTnkIf_mqziMf&jf&jzi$kIq"d3mIe<xjFnMGgj k"^p[mIfe<fFM:j"m&mIj k mIdWilmIdWiMmhn%~eb^pGmIfng[mIe<xe<Vjzo6nMkf&gj jzo
A PROPERTY OF THE FIBONACCI SEQUENCE (Fm), m = 0, 1,
, 1980
"... It Is well known that the sequence of the (natural) logarithms reduced mod 1 of the terms Fm of the Fibonacci sequence are dense in the unit interval. See [1], [2]. This is also the case when the logarithms are taken with respect to a base b, where b is a positive integer _> 2. In order to see th ..."
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It Is well known that the sequence of the (natural) logarithms reduced mod 1 of the terms Fm of the Fibonacci sequence are dense in the unit interval. See [1], [2]. This is also the case when the logarithms are taken with respect to a base b, where b is a positive integer _> 2. In order to see
$ \sigma_k(F_m) = F_n $ σ k (F
, 2010
"... Abstract. Let σ k (n) be the sum of the kth powers of the divisors of n. Here, we prove that if (Fn) n≥1 is the Fibonacci sequence, then the only solutions of the equation σ k (Fm) = Fn in positive integers k ≥ 2, m and n have k = 2 and m ∈ {1, 2, 3}. The proof uses linear forms in two and three lo ..."
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Abstract. Let σ k (n) be the sum of the kth powers of the divisors of n. Here, we prove that if (Fn) n≥1 is the Fibonacci sequence, then the only solutions of the equation σ k (Fm) = Fn in positive integers k ≥ 2, m and n have k = 2 and m ∈ {1, 2, 3}. The proof uses linear forms in two and three
Results 1  10
of
155