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P08 [Algebra] - Turkish NMO 1st Round - 2002

Source:

August 8, 2014
algebrapolynomialgeometry3D geometry

Problem Statement

Which of the following polynomials does not divide x60−1x^{60} - 1?
<spanclass=′latex−bold′>a)</span> x2+x+1<spanclass=′latex−bold′>b)</span> x4−1<spanclass=′latex−bold′>c)</span> x5−1<spanclass=′latex−bold′>d)</span> x15−1<spanclass=′latex−bold′>e)</span> None of above <span class='latex-bold'>a)</span>\ x^2+x+1 \qquad<span class='latex-bold'>b)</span>\ x^4-1 \qquad<span class='latex-bold'>c)</span>\ x^5-1 \qquad<span class='latex-bold'>d)</span>\ x^{15}-1 \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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