Exponent al lui 2 in diferenta de combinari

Moderators: Laurian Filip, Filip Chindea, maky, Cosmin Pohoata

Post Reply
User avatar
Filip Chindea
Newton
Posts: 324
Joined: Thu Sep 27, 2007 9:01 pm
Location: Bucharest

Exponent al lui 2 in diferenta de combinari

Post by Filip Chindea »

Pentru orice intreg \( k \ge 2 \), aratati ca exponentul

\( v_2\left( {2^{k + 1} \choose 2^k} - {2^k \choose 2^{k-1}} \right) = 3k \).

[ IMO Shortlist 2007, N4 ]
Life is complex: it has real and imaginary components.
Top
Post Reply

Return to “Teoria Numerelor”