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Turkish NMO First Round - 1999 P-26 (Number Theory)

Source:

July 3, 2012

Problem Statement

Let x x, y y, z z be integers such that \begin{array}{l} {x \minus{} 3y \plus{} 2z \equal{} 1} \\ {2x \plus{} y \minus{} 5z \equal{} 7} \end{array} Then z z can be
<spanclass=′latex−bold′>(A)</span> 3111<spanclass=′latex−bold′>(B)</span> 4111<spanclass=′latex−bold′>(C)</span> 5111<spanclass=′latex−bold′>(D)</span> 6111<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 3^{111} \qquad<span class='latex-bold'>(B)</span>\ 4^{111} \qquad<span class='latex-bold'>(C)</span>\ 5^{111} \qquad<span class='latex-bold'>(D)</span>\ 6^{111} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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