MathDB
P27 [Algebra] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014
function

Problem Statement

Let ff be a function defined on positive integers such that f(1)=4f(1)=4, f(2n)=f(n)f(2n)=f(n) and f(2n+1)=f(n)+2f(2n+1)=f(n)+2 for every positive integer nn. For how many positive integers kk less than 20142014, it is f(k)=8f(k)=8?
<spanclass=latexbold>(A)</span> 45<spanclass=latexbold>(B)</span> 120<spanclass=latexbold>(C)</span> 165<spanclass=latexbold>(D)</span> 180<spanclass=latexbold>(E)</span> 215 <span class='latex-bold'>(A)</span>\ 45 \qquad<span class='latex-bold'>(B)</span>\ 120 \qquad<span class='latex-bold'>(C)</span>\ 165 \qquad<span class='latex-bold'>(D)</span>\ 180 \qquad<span class='latex-bold'>(E)</span>\ 215