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Turkish NMO First Round - 1999 P-02 (Number Theory)

Source:

July 3, 2012

Problem Statement

How many ordered integer pairs (x,y) \left(x,y\right) are there such that xy \equal{} 4\left(y^{2} \plus{} x\right)?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 14 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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