Difference between revisions of "2023 IMO Problems/Problem 3"
(Created page with "==Problem== For each integer <math>k \geqslant 2</math>, determine all infinite sequences of positive integers <math>a_1, a_2, \ldots</math> for which there exists a polynomia...") |
(→Solution) |
||
| Line 6: | Line 6: | ||
==Solution== | ==Solution== | ||
https://www.youtube.com/watch?v=JhThDz0H7cI [Video contains solutions to all day 1 problems] | https://www.youtube.com/watch?v=JhThDz0H7cI [Video contains solutions to all day 1 problems] | ||
| + | https://www.youtube.com/watch?v=SP-7LgQh0uY [Video contains solution to problem 3] | ||
Revision as of 10:49, 3 October 2023
Problem
For each integer 
, determine all infinite sequences of positive integers 
for which there exists a polynomial 
of the form 
, where 
are non-negative integers, such that
![\[P\left(a_n\right)=a_{n+1} a_{n+2} \cdots a_{n+k}\]](http://latex.artofproblemsolving.com/8/6/e/86e9095fe41091db78cfab1b7c22211df21037aa.png)
for every integer 
.
Solution
https://www.youtube.com/watch?v=JhThDz0H7cI [Video contains solutions to all day 1 problems] https://www.youtube.com/watch?v=SP-7LgQh0uY [Video contains solution to problem 3]
