Submultimi si divizibilitate

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Submultimi si divizibilitate

Post by Filip Chindea »

Fie \( X \) un set de \( 10^4 \) de intregi nedivizibili prin \( 47 \). Aratati ca exista un subset \( Y \) de \( 2007 \) elemente ale lui \( X \) astfel incat \( a - b + c - d + e \) este nedivizibil prin \( 47 \) oricare ar fi \( a, b, c, d, e \in Y \).

[ IMO Shortlist 2007, N3 ]
Life is complex: it has real and imaginary components.
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