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Fungrim entry: da45c0

gcd ⁣(Fm,Fn)=Fgcd(m,n)\gcd\!\left(F_{m}, F_{n}\right) = F_{\gcd\left(m, n\right)}
Assumptions:mZ  and  nZm \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
\gcd\!\left(F_{m}, F_{n}\right) = F_{\gcd\left(m, n\right)}

m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(GCD(Fibonacci(m), Fibonacci(n)), Fibonacci(GCD(m, 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