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Turkish NMO First Round - 2012 Problem - 22 {Number Theory}

Source:

July 1, 2012
symmetry

Problem Statement

How many integer pairs (m,n)(m,n) are there satisfying 4mn(m+n1)=(m2+1)(n2+1)4mn(m+n-1)=(m^2+1)(n^2+1)?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 2<spanclass=latexbold>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 5 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 3 \qquad <span class='latex-bold'>(D)</span>\ 2 \qquad <span class='latex-bold'>(E)</span>\ 1