Search Results for ""

The identity F_n^4-F_(n-2)F_(n-1)F_(n+1)F_(n+2)=1, where F_n is a Fibonacci number.

The sequence of Fibonacci numbers {F_n} is periodic modulo any modulus m (Wall 1960), and the period (mod m) is the known as the Pisano period pi(m) (Wrench 1969). For m=1, ...

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

A trigonal trapezohedron, also called a trigonal deltohedron, is a polyhedron formed by six congruent rhombi. Special cases include the cube, acute golden rhombohedron, and ...

Closed forms are known for the sums of reciprocals of even-indexed Lucas numbers P_L^((e)) = sum_(n=1)^(infty)1/(L_(2n)) (1) = sum_(n=1)^(infty)1/(phi^(2n)+phi^(-2n)) (2) = ...

The sequence {F_n-1} is complete even if restricted to subsequences which contain no two consecutive terms, where F_n is a Fibonacci number.

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

A generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation ...

A number having 666 digits (where 666 is the beast number) is called an apocalypse number. The Fibonacci number F_(3184) is the smallest Fibonacci apocalypse number (Livio ...

The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).