Plane netrecand prin origine

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Plane netrecand prin origine

Post by Filip Chindea »

Fie un intreg \( n > 1 \). Consideram setul

\( S = \left\{ (x, y, z) \ : \ x, y, z \in \overline{0, n}, x + y + z > 0 \right\} \).

Sa se gaseasca cel mai mic numar de plane cu proprietatea ca reuniunea lor include pe \( S \) dar nu si originea.

[ IMO 2007/6, Shortlist A7 ]
Life is complex: it has real and imaginary components.
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