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Fungrim entry: a104b0

Fm+n=FmFn+1+Fm1FnF_{m + n} = F_{m} F_{n + 1} + F_{m - 1} F_{n}
Assumptions:mZ  and  nZm \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
F_{m + n} = F_{m} F_{n + 1} + F_{m - 1} F_{n}

m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(Fibonacci(Add(m, n)), Add(Mul(Fibonacci(m), Fibonacci(Add(n, 1))), Mul(Fibonacci(Sub(m, 1)), Fibonacci(n))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZ), 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.

2021-03-15 19:12:00.328586 UTC