Problem

Source: China Girls Math Olympiad 2008, Problem 8

Tags: search, number theory unsolved, number theory



For positive integers $ n$, $ f_n = \lfloor2^n\sqrt {2008}\rfloor + \lfloor2^n\sqrt {2009}\rfloor$. Prove there are infinitely many odd numbers and infinitely many even numbers in the sequence $ f_1,f_2,\ldots$.