MathDB
Turkey NMO 2008 1st Round - P18 (Number Theory)

Source:

August 25, 2012
quadratics

Problem Statement

How many positive integers nn are there such that n+n+n+n\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n}}}} is an integer?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> Infinitely many<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}