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With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [57] As a result, 8 and 144 (F 6 and F 12) are the only Fibonacci numbers that are the product of other Fibonacci numbers. [58]
The Sharp EL-8, also known as the ELSI-8, [1] was one of the earliest mass-produced hand-held electronic calculators [1] and the first hand-held calculator to be made by Sharp. Introduced around the start of 1971, [ note 1 ] it was based on Sharp's preceding QT-8D and QT-8B compact desktop calculators and used the same logic circuits, but it ...
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
4.13.1: 13 June 2024 [10] Free GNU GPL [11] Specialized CAS for group theory and combinatorics. GeoGebra CAS: Markus Hohenwarter et al. 2013 6.0.753.0: 3 January 2023: Free for non-commercial use [12] Freeware [12] Web-based or Desktop CAS Calculator GiNaC: Christian Bauer, Alexander Frink, Richard B. Kreckel, et al. 1999 1999 1.8.3: 23 March ...
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
The book contains specific algebraic explanations for each of the above operations. Most of the information in this article is from the original book. The algorithms/operations for multiplication, etc., can be expressed in other more compact ways that the book does not specify, despite the chapter on algebraic description.
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If n is a power of an odd prime number the formula for the totient says its totient can be a power of two only if n is a first power and n − 1 is a power of 2. The primes that are one more than a power of 2 are called Fermat primes , and only five are known: 3, 5, 17, 257, and 65537.