Fibonacci数列关于整除的若干性质
number theory/ Binet formulasLucas p-numbersnatural sciencemathematical apparatusgeneralized Fibonacci p-numbersPascal triangleanalytical formulasclassical Fibonacci numbersrecurrent sequences/ B0250 Combinatorial mathematics C1160 Combinatorial mathematicsModern natural science requires the development of new ...
What is the Fibonacci sequence? Learn about the Fibonacci sequence definition, the golden ratio in nature, the Fibonacci spiral, and Fibonacci...
Consider thePisano Periodsderived from the Fibonacci sequence. A Pisano Period, named after Fibonacci himself, is a set of numbers that cyclically repeat themselves. The numbers are remainders obtained from the division of Fibonacci numbers and a positive real number. One can divide the sequence wi...
the ratio between succeeding numbers approached the numberα,thegolden ratio, whosevalueis 1.6180…, or (1 +√5)/2. In the 19th century the termFibonacci sequencewas coined by the French mathematicianEdouard Lucas, and scientists began to discover such sequences in nature; for example, in the...
The first two equations are essentially stating that the term in the first position equals 0 and the term in the second position equals 1. The third equation is a recursive formula, which means that each number of the sequence is defined by using the preceding numbers. For example, to defin...
Mathematics - Number Theory11B39It is shown that there are no non-trivial fifth-, seventh-, eleventh-, thirteenth- or seventeenth powers in the Fibonacci sequence. For eleventh, thirteenth- and seventeenth powers an alternative (to the usual exhaustive check of products of powers of fundamental ...
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How does congruency work in elementary number theory? Choose two numbers other than 1 and 1. The numbers do not have to be equal. Generate a Fibonacci-like sequence, beginning with these two numbers. Write the first ten terms of your sequence. For example, you could choose the numbers 5 ...
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It is closely related to the golden ratio, which appears in various natural and artistic contexts. The sequence is used in financial markets to predict price movements through techniques like ...