MathDB

10

Part of 2006 National Olympiad First Round

Problems(1)

Turkey NMO 2006 1st Round - P10 (Number Theory)

Source:

2/2/2013
What is the larget integer nn such that 5n5^n divides 2006!(1003!)2\frac {2006!}{(1003!)^2}?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 500 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 500