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April 21, 2009

Problem Statement

How many pairs of real numbers (x,y) \left(x,y\right) are there such that x^{4} \minus{} 2^{ \minus{} y^{2} } x^{2} \minus{} \left\| x^{2} \right\| \plus{} 1 \equal{} 0, where a \left\| a\right\| denotes the greatest integer not exceeding a a.
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> Infinitely many<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}