Difference between revisions of "2017 IMO Problems/Problem 1"
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Revision as of 01:19, 19 November 2023
Problem
For each integer 
, define the sequence 
for 
as
![\[a_{n+1} = \begin{cases} \sqrt{a_n} & \text{if } \sqrt{a_n} \text{ is an integer,} \\ a_n + 3 & \text{otherwise.} \end{cases}\]](http://latex.artofproblemsolving.com/7/e/5/7e5005fa83196dcdb7e5270b0dc20e1f13e22bd4.png)
Determine all values of 
such that there exists a number 
such that 
for infinitely many values of 
.
Solution
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
| 2017 IMO (Problems) • Resources | ||
| Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
