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P22 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 18, 2013

Problem Statement

For how many integers 0≤n<20130\leq n < 2013, is n4+2n3−20n2+2n−21n^4+2n^3-20n^2+2n-21 divisible by 20132013?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 8<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 16<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 6 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 16 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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