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Turkey NMO 2007 1st Round - P14 (Number Theory)

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October 4, 2012

Problem Statement

What is the largest integer nn that satisfies (1002−992)(992−982)…(32−22)(22−12)(100^2-99^2)(99^2-98^2)\dots(3^2-2^2)(2^2-1^2) is divisible by 3n3^n?
<spanclass=′latex−bold′>(A)</span> 49<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 97<spanclass=′latex−bold′>(D)</span> 103<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 49 \qquad<span class='latex-bold'>(B)</span>\ 53 \qquad<span class='latex-bold'>(C)</span>\ 97 \qquad<span class='latex-bold'>(D)</span>\ 103 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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