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Fungrim entry: 80f20f

gcd⁡ ⁣(a,a−2)=1+1+(−1)a2\gcd\!\left(a, a - 2\right) = 1 + \frac{1 + {\left(-1\right)}^{a}}{2}
Assumptions:a∈Za \in \mathbb{Z}
TeX:
\gcd\!\left(a, a - 2\right) = 1 + \frac{1 + {\left(-1\right)}^{a}}{2}

a \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GCDgcd⁡ ⁣(n,k)\gcd\!\left(n, k\right) Greatest common divisor
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("80f20f"),
    Formula(Equal(GCD(a, Sub(a, 2)), Add(1, Div(Add(1, Pow(-1, a)), 2)))),
    Variables(a),
    Assumptions(Element(a, ZZ)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC