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P30 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 18, 2013
modular arithmetic

Problem Statement

For how many postive integers nn less than 20132013, does p2+p+1p^2+p+1 divide nn where pp is the least prime divisor of nn?
<spanclass=′latex−bold′>(A)</span> 212<spanclass=′latex−bold′>(B)</span> 206<spanclass=′latex−bold′>(C)</span> 191<spanclass=′latex−bold′>(D)</span> 185<spanclass=′latex−bold′>(E)</span> 173 <span class='latex-bold'>(A)</span>\ 212 \qquad<span class='latex-bold'>(B)</span>\ 206 \qquad<span class='latex-bold'>(C)</span>\ 191 \qquad<span class='latex-bold'>(D)</span>\ 185 \qquad<span class='latex-bold'>(E)</span>\ 173
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