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: 4

2023 Mexico National Olympiad, 3
Tags: geometry , 2023 , P3 , Mexico , Hi
Let $ABCD$ be a convex quadrilateral. If $M, N, K$ are the midpoints of the segments $AB, BC$, and $CD$, respectively, and there is also a point $P$ inside the quadrilateral $ABCD$ such that, $\angle BPN= \angle PAD$ and $\angle CPN=\angle PDA$. Show that $AB \cdot CD=4PM\cdot PK$.

1990 IMO Shortlist, 23
Tags: modular arithmetic , number theory , Divisibility , IMO 1990 , Orders And LTE , P3
Determine all integers $ n > 1$ such that \[ \frac {2^n \plus{} 1}{n^2} \] is an integer.

1990 IMO, 3
Tags: modular arithmetic , number theory , Divisibility , IMO 1990 , Orders And LTE , P3
Determine all integers $ n > 1$ such that \[ \frac {2^n \plus{} 1}{n^2} \] is an integer.

1990 IMO Longlists, 79
Tags: modular arithmetic , number theory , Divisibility , IMO 1990 , Orders And LTE , P3
Determine all integers $ n > 1$ such that \[ \frac {2^n \plus{} 1}{n^2} \] is an integer.