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Fungrim entry: ab563e

Fn2=Fn+mFn−m+(−1)n+mFm2F_{n}^{2} = F_{n + m} F_{n - m} + {\left(-1\right)}^{n + m} F_{m}^{2}
Catalan's identity
Assumptions:n∈Z  and⁡  m∈Zn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}
TeX:
F_{n}^{2} = F_{n + m} F_{n - m} + {\left(-1\right)}^{n + m} F_{m}^{2}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \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("ab563e"),
    Formula(Equal(Pow(Fibonacci(n), 2), Add(Mul(Fibonacci(Add(n, m)), Fibonacci(Sub(n, m))), Mul(Pow(-1, Add(n, m)), Pow(Fibonacci(m), 2))))),
    Description("Catalan'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