✦ LIBER ✦

Sums of Factorials in Binary Recurrence Sequences

✍ Scribed by George Grossman; Florian Luca

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 141 KB
Volume: 93
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2718

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider the problem of expressing a term of a given nondegenerate binary recurrence sequence as a sum of factorials. We show that if one bounds the number of factorials allowed, then there are only finitely many effectively computable terms which can be represented in this way. As an application, we also find the largest members of the classical Fibonacci and Lucas sequences which can be written as a sum or a difference of two factorials.

📜 SIMILAR VOLUMES

Sections and Lacunary Sums of Linearly R

Sections and Lacunary Sums of Linearly Recurrent Sequences

✍ Luis Verde-Star 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 132 KB

The Product of Like-Indexed Terms in Bin

The Product of Like-Indexed Terms in Binary Recurrences

✍ F. Luca; P.G. Walsh 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 188 KB

In recent work by Hajdu and Szalay, Diophantine equations of the form ða k À 1Þðb k À 1Þ ¼ x 2 were completely solved for a few pairs ða; bÞ: In this paper, a general finiteness theorem for equations of the form u k v k ¼ x n is proved, where u k and v k are terms in certain types of binary recurren

Factorial experiments in sequence: The a

Factorial experiments in sequence: The attainment of optimum conditions for a decontamination process

✍ M. K. Barnett; P. M. Hamilton; F. C. Mead Jr. 📂 Article 📅 1956 🏛 American Institute of Chemical Engineers 🌐 English ⚖ 795 KB

The ABC Conjecture and the Powerful Part

The ABC Conjecture and the Powerful Part of Terms in Binary Recurring Sequences

✍ Paulo Ribenboim; Gary Walsh 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 130 KB

We consider non-degenerate binary recurring sequences with positive discriminant, relatively prime parameters, and whose initial terms satisfy a certain divisibility condition. Assuming that the ABC conjecture is true, we show that the powerful part of the terms of the sequence remain ``small.'' In

Detection of linear substructures in cal

Detection of linear substructures in calibration model by robust approach: Maximum sum of binary-coded residuals (MASBR) regression

✍ Ji-Hong Wang; Jian-Hui Jiang; Ru-Qin Yu 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 531 KB

The MASBR (maximum sum of binary-coded residuals) procedure proposed previously as a robust regression method has been modified and applied to find the linear substructures in a data set. A graphic approach is used to identify the acceptable error limit (AEL) in the MASBR algorithm. Some data sets w

Decoding of multichannel EEG activity fr

Decoding of multichannel EEG activity from the visual cortex in response to pseudorandom binary sequences of visual stimuli

✍ Hooman Nezamfar; Umut Orhan; Shalini Purwar; Kenneth Hild; Barry Oken; Deniz Erd 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 495 KB

## Abstract Electroencephalography (EEG) signals have been an attractive choice to build noninvasive brain computer interfaces (BCIs) for nearly three decades. Depending on the stimuli, there are different responses which one could get from EEG signals. One of them is the P300 response which is a v