This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
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NO:

Found problems: 2

2020 APMO, 2
Tags: APMO 2020
Show that $r = 2$ is the largest real number $r$ which satisfies the following condition: If a sequence $a_1$, $a_2$, $\ldots$ of positive integers fulfills the inequalities \[a_n \leq a_{n+2} \leq\sqrt{a_n^2+ra_{n+1}}\] for every positive integer $n$, then there exists a positive integer $M$ such that $a_{n+2} = a_n$ for every $n \geq M$.

2020 Brazil Team Selection Test, 2
Tags: APMO 2020
Show that $r = 2$ is the largest real number $r$ which satisfies the following condition: If a sequence $a_1$, $a_2$, $\ldots$ of positive integers fulfills the inequalities \[a_n \leq a_{n+2} \leq\sqrt{a_n^2+ra_{n+1}}\] for every positive integer $n$, then there exists a positive integer $M$ such that $a_{n+2} = a_n$ for every $n \geq M$.