2017 IMO Problems/Problem 1

Problem

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 $a_0$ such that there exists a number $A$ such that $a_n = A$ for infinitely many values of $n$ .

Solution

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2017 IMO (Problems) • Resources
Preceded by First Problem	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 2
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2017 IMO Problems/Problem 1

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