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Fungrim entry: 9d26d2

{Fn:n∈Z≥0  and⁡  Fn∈Z}={F0,F1,F2,F12}={0,1,144}\left\{ F_{n} : n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; \sqrt{F_{n}} \in \mathbb{Z} \right\} = \left\{F_{0}, F_{1}, F_{2}, F_{12}\right\} = \left\{0, 1, 144\right\}
TeX:
\left\{ F_{n} : n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; \sqrt{F_{n}} \in \mathbb{Z} \right\} = \left\{F_{0}, F_{1}, F_{2}, F_{12}\right\} = \left\{0, 1, 144\right\}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Sqrtz\sqrt{z} Principal square root
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("9d26d2"),
    Formula(Equal(Set(Fibonacci(n), For(n), And(Element(n, ZZGreaterEqual(0)), Element(Sqrt(Fibonacci(n)), ZZ))), Set(Fibonacci(0), Fibonacci(1), Fibonacci(2), Fibonacci(12)), Set(0, 1, 144))))

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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