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P22 [Number Theory] - Turkish NMO 1st Round - 2004

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November 15, 2013

Problem Statement

For which of the following expressions, there exists an integer xx such that the expression is divisble by 2525?
<spanclass=′latex−bold′>(A)</span> x3−3x2+8x−1<spanclass=′latex−bold′>(B)</span> x3+3x2−2x+1<spanclass=′latex−bold′>(C)</span> x3+14x2+3x−8<spanclass=′latex−bold′>(D)</span> x3−5x2+x+1<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ x^3-3x^2+8x-1 \\ \qquad<span class='latex-bold'>(B)</span>\ x^3+3x^2-2x+1 \\ \qquad<span class='latex-bold'>(C)</span>\ x^3+14x^2+3x-8 \\ \qquad<span class='latex-bold'>(D)</span>\ x^3-5x^2+x+1 \\ \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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