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

2000 Austrian-Polish Competition, 6
Tags: 3D geometry , geometry , combinatorics , cubes
Consider the solid $Q$ obtained by attaching unit cubes $Q_1...Q_6$ at the six faces of a unit cube $Q$. Prove or disprove that the space can be filled up with such solids so that no two of them have a common interior point.

2022 Olimphíada, 1
Tags: number theory , cubes
Let $n$ and $p$ be positive integers, with $p>3$ prime, such that: i) $n\mid p-3;$ ii) $p\mid (n+1)^3-1.$ Show that $pn+1$ is the cube of an integer.