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

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Found problems: 2

2009 Peru Iberoamerican Team Selection Test, P1
A set $P$ has the following property: “For any positive integer $k$, if $p$ is a prime factor of $k^3+6$, then $p$ belongs to $P$ ”. Prove that $P$ is infinite.
schur number theory bijection modular arithmetic

2006 Hong kong National Olympiad, 1
A subset $M$ of $\{1, 2, . . . , 2006\}$ has the property that for any three elements $x, y, z$ of $M$ with $x < y < z$, $x+ y$ does not divide $z$. Determine the largest possible size of $M$.
ramsey theory schur combinatorics Ramsey theory