MathDB
Turkey NMO 2010 1st Round - P02 (Number Theory)

Source:

July 27, 2012
linear algebramatrix

Problem Statement

How many ordered pairs of positive integers (x,y)(x,y) are there such that y2x2=2y+7x+4y^2-x^2=2y+7x+4?
<spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 1<spanclass=latexbold>(D)</span> 0<spanclass=latexbold>(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}