MathDB
P26 [Number Theory] - Turkish NMO 1st Round - 2005

Source:

October 26, 2013

Problem Statement

For every positive integer nn, f(2n+1)=2f(2n)f(2n+1)=2f(2n), f(2n)=f(2n1)+1f(2n)=f(2n-1)+1, and f(1)=0f(1)=0. What is the remainder when f(2005)f(2005) is divided by 55?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4