MathDB
Turkey NMO 2010 1st Round - P14 (Number Theory)

Source:

July 27, 2012

Problem Statement

A grasshopper jumps either 364364 or 715715 units on the real number line. If it starts from the point 00, what is the smallest distance that the grasshoper can be away from the point 20102010?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 8<spanclass=latexbold>(C)</span> 18<spanclass=latexbold>(D)</span> 34<spanclass=latexbold>(E)</span> 164 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 18 \qquad<span class='latex-bold'>(D)</span>\ 34 \qquad<span class='latex-bold'>(E)</span>\ 164