MathDB
P14 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014

Problem Statement

Let x1,x2,,xnx_1, x_2, \dots, x_n be a positive integer sequence such that each term is less than or equal to 20012001 and for every i3i\geq 3, xi=xi1xi2x_i = |x_{i-1}-x_{i-2}|. What is the largest possible value of nn?
<spanclass=latexbold>(A)</span> 1000<spanclass=latexbold>(B)</span> 2001<spanclass=latexbold>(C)</span> 3002<spanclass=latexbold>(D)</span> 4003<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 1000 \qquad<span class='latex-bold'>(B)</span>\ 2001 \qquad<span class='latex-bold'>(C)</span>\ 3002 \qquad<span class='latex-bold'>(D)</span>\ 4003 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}