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.

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Found problems: 2

2025 Bangladesh Mathematical Olympiad, P4
Tags: ad hoc , modular arithmetic , number theory
Let set $S$ be the smallest set of positive integers satisfying the following properties: [list] [*] $2$ is in set $S$. [*] If $n^2$ is in set $S$, then $n$ is also in set $S$. [*] If $n$ is in set $S$, then $(n+5)^2$ is also in set $S$. [/list] Determine which positive integers are not in set $S$.

2023 Serbia Team Selection Test, P1
Tags: combinatorics , extremal graph theory , ad hoc , graph theory
In a simple graph with 300 vertices no two vertices of the same degree are adjacent (boo hoo hoo). What is the maximal possible number of edges in such a graph?