MathDB
Rational roots

Source: 0

April 21, 2009

Problem Statement

How many pairs of rational number (x,y) \left(x,y\right) are there satisfying the equation y \equal{} \sqrt {x^{2} \plus{} \frac {1}{1999} }?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<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>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}