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P19 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014
modular arithmetic

Problem Statement

If the integers m,n,km,n,k hold the equation 221m+247n+323k=2001221m+247n+323k=2001, what is the smallest possible value of kk greater than 100100?
<spanclass=′latex−bold′>(A)</span> 124<spanclass=′latex−bold′>(B)</span> 111<spanclass=′latex−bold′>(C)</span> 107<spanclass=′latex−bold′>(D)</span> 101<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 124 \qquad<span class='latex-bold'>(B)</span>\ 111 \qquad<span class='latex-bold'>(C)</span>\ 107 \qquad<span class='latex-bold'>(D)</span>\ 101 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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