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Turkey NMO 2010 1st Round - P06 (Number Theory)

Source:

July 27, 2012

Problem Statement

How many ordered pairs of integers (x,y)(x,y) are there such that 2011y2=2010x+32011y^2=2010x+3?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 0<spanclass=′latex−bold′>(E)</span> Infinitely many <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 1 \qquad<span class='latex-bold'>(D)</span>\ 0 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}
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