MathDB
P34 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014
function

Problem Statement

Let ff be a real-valued function defined over ordered pairs of integers such that f(x+3m2n,y4m+5n)=f(x,y)f(x+3m-2n, y-4m+5n) = f(x,y) for every integers x,y,m,nx,y,m,n. At most how many elements does the range set of ff have?
<spanclass=latexbold>(A)</span> 7<spanclass=latexbold>(B)</span> 8<spanclass=latexbold>(C)</span> 15<spanclass=latexbold>(D)</span> 49<spanclass=latexbold>(E)</span> Infinitely many <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 15 \qquad<span class='latex-bold'>(D)</span>\ 49 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}