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P11 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014
quadraticsVietaSFFT

Problem Statement

For how many integers nn, does the equation system 2x+3y=75x+ny=n2\begin{array}{rcl} 2x+3y &=& 7\\ 5x + ny &=& n^2 \end{array} have a solution over integers?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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