Difference between revisions of "2024 IMO Problems/Problem 3"
(Created page with "Let <math>a_1, a_2, a_3, \dots</math> be an infinite sequence of positive integers, and let <math>N</math> be a positive integer. Suppose that, for each <math>n > N</math>, <m...") |
|||
(One intermediate revision by the same user not shown) | |||
Line 4: | Line 4: | ||
(An infinite sequence <math>b_1, b_2, b_3, \dots</math> is eventually periodic if there exist positive integers <math>p</math> and <math>M</math> such that <math>b_{m+p} = b_m</math> for all <math>m \ge M</math>.) | (An infinite sequence <math>b_1, b_2, b_3, \dots</math> is eventually periodic if there exist positive integers <math>p</math> and <math>M</math> such that <math>b_{m+p} = b_m</math> for all <math>m \ge M</math>.) | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/ASV1dZCuWGs (in full detail!) |
Latest revision as of 05:33, 18 July 2024
Let be an infinite sequence of positive integers, and let
be a positive integer. Suppose that, for each
,
is equal to the number of times
appears in the list
.
Prove that at least one of the sequence and
is eventually periodic.
(An infinite sequence is eventually periodic if there exist positive integers
and
such that
for all
.)
Video Solution
https://youtu.be/ASV1dZCuWGs (in full detail!)