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Fungrim entry: 301081

FmFn+1−Fm+1Fn=(−1)nFm−nF_{m} F_{n + 1} - F_{m + 1} F_{n} = {\left(-1\right)}^{n} F_{m - n}
d'Ocagne's identity
Assumptions:n∈Z  and⁡  m∈Zn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}
TeX:
F_{m} F_{n + 1} - F_{m + 1} F_{n} = {\left(-1\right)}^{n} F_{m - n}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("301081"),
    Formula(Equal(Sub(Mul(Fibonacci(m), Fibonacci(Add(n, 1))), Mul(Fibonacci(Add(m, 1)), Fibonacci(n))), Mul(Pow(-1, n), Fibonacci(Sub(m, n))))),
    Description("d'Ocagne's identity"),
    Variables(n, m),
    Assumptions(And(Element(n, ZZ), Element(m, ZZ))))

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2021-03-15 19:12:00.328586 UTC