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Turkey NMO 2010 1st Round - P10 (Number Theory)

Source:

July 27, 2012
modular arithmetic

Problem Statement

How many integers nn with 0≤n<8400\leq n < 840 are there such that 840840 divides n8−n4+n−1n^8-n^4+n-1?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 8
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