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Turkish NMO First Round - 2000 P-30 (Number Theory)

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July 8, 2012

Problem Statement

How many ordered integer pairs (x,y)(x,y) (0≤x,y<310\leq x,y < 31) are there satisfying (x2−18)2≡y2(mod  31)(x^2-18)^2\equiv y^2 (\mod 31)?
<spanclass=′latex−bold′>(A)</span> 59<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 61<spanclass=′latex−bold′>(D)</span> 62<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 59 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 61 \qquad<span class='latex-bold'>(D)</span>\ 62 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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