IMO $2017$ P$1$

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IMO $2017$ P$1$

Post Number:#1  Unread postby ahmedittihad » Wed Jul 19, 2017 12:25 am

For each integer $a_0 > 1$, define the sequence $a_0, a_1, a_2, \ldots$ for $n \geq 0$ as
$$a_{n+1} =
\begin{cases}
\sqrt{a_n} & \text{if } \sqrt{a_n} \text{ is an integer,} \\
a_n + 3 & \text{otherwise.}
\end{cases}
$$
Determine all values of $a_0$ so that there exists a number $A$ such that $a_n = A$ for infinitely many values of $n$.
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Re: IMO $2017$ P$1$

Post Number:#2  Unread postby Katy729 » Fri Aug 04, 2017 1:25 pm

Anyone?? :(
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