Exponent al lui 2 in diferenta de combinari
Posted: Sun Jul 13, 2008 8:39 pm
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 ]
\( v_2\left( {2^{k + 1} \choose 2^k} - {2^k \choose 2^{k-1}} \right) = 3k \).
[ IMO Shortlist 2007, N4 ]