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Fungrim entry: 8db61e

Fn+iFn+j−FnFn+i+j=(−1)nFiFjF_{n + i} F_{n + j} - F_{n} F_{n + i + j} = {\left(-1\right)}^{n} F_{i} F_{j}
Vajda's identity
Assumptions:n∈Z  and⁡  i∈Z  and⁡  j∈Zn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; i \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; j \in \mathbb{Z}
TeX:
F_{n + i} F_{n + j} - F_{n} F_{n + i + j} = {\left(-1\right)}^{n} F_{i} F_{j}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; i \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; j \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("8db61e"),
    Formula(Equal(Sub(Mul(Fibonacci(Add(n, i)), Fibonacci(Add(n, j))), Mul(Fibonacci(n), Fibonacci(Add(Add(n, i), j)))), Mul(Mul(Pow(-1, n), Fibonacci(i)), Fibonacci(j)))),
    Description("Vajda's identity"),
    Variables(n, i, j),
    Assumptions(And(Element(n, ZZ), Element(i, ZZ), Element(j, ZZ))))

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2021-03-15 19:12:00.328586 UTC