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Fungrim entry: 073466

Fn2=Fn+1Fn1(1)nF_{n}^{2} = F_{n + 1} F_{n - 1} - {\left(-1\right)}^{n}
Cassini's identity
Assumptions:nZn \in \mathbb{Z}
TeX:
F_{n}^{2} = F_{n + 1} F_{n - 1} - {\left(-1\right)}^{n}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("073466"),
    Formula(Equal(Pow(Fibonacci(n), 2), Sub(Mul(Fibonacci(Add(n, 1)), Fibonacci(Sub(n, 1))), Pow(-1, n)))),
    Description("Cassini's identity"),
    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