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Finding the Smallest Reducible Fraction

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March 8, 2009
algorithmnumber theoryEuclidean algorithm

Problem Statement

Find the least positive integer n n for which \frac{n\minus{}13}{5n\plus{}6} is non-zero reducible fraction. <spanclass=′latex−bold′>(A)</span> 45<spanclass=′latex−bold′>(B)</span> 68<spanclass=′latex−bold′>(C)</span> 155<spanclass=′latex−bold′>(D)</span> 226<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ 45 \qquad <span class='latex-bold'>(B)</span>\ 68 \qquad <span class='latex-bold'>(C)</span>\ 155 \qquad <span class='latex-bold'>(D)</span>\ 226 \qquad <span class='latex-bold'>(E)</span>\ \text{none of these}
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