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Turkey NMO 2006 1st Round - P20 (Combinatorics)

Source:

February 2, 2013

Problem Statement

The integer kk is a good number, if we can divide a square into kk squares. How many good numbers not greater than 20062006 are there?
<spanclass=latexbold>(A)</span> 1003<spanclass=latexbold>(B)</span> 1026<spanclass=latexbold>(C)</span> 2000<spanclass=latexbold>(D)</span> 2003<spanclass=latexbold>(E)</span> 2004 <span class='latex-bold'>(A)</span>\ 1003 \qquad<span class='latex-bold'>(B)</span>\ 1026 \qquad<span class='latex-bold'>(C)</span>\ 2000 \qquad<span class='latex-bold'>(D)</span>\ 2003 \qquad<span class='latex-bold'>(E)</span>\ 2004