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Fungrim entry: 0e2425

(Fn+1Fn)=(1110)(FnFn1)\begin{pmatrix} F_{n + 1} \\ F_{n} \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} F_{n} \\ F_{n - 1} \end{pmatrix}
Assumptions:nZn \in \mathbb{Z}
TeX:
\begin{pmatrix} F_{n + 1} \\ F_{n} \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} F_{n} \\ F_{n - 1} \end{pmatrix}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("0e2425"),
    Formula(Equal(Matrix2x1(Fibonacci(Add(n, 1)), Fibonacci(n)), Mul(Matrix2x2(1, 1, 1, 0), Matrix2x1(Fibonacci(n), Fibonacci(Sub(n, 1)))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC