OSN 2008 Problem 4

Let $A = \{1,2,\ldots,2008\}$ a) Find the number of subset of $A$ which satisfy : the product of its elements is divisible by 7 b) Let $N(i)$ denotes the number of subset of $A$ which sum of its elements remains $i$ when divided by 7. Prove that $N(0) - N(1) + N(2) - N(3) + N(4) - N(5) + N(6)-N(7) = 0$

EDITED : thx for cosinator.. BTW, your statement and my correction give 80% hint of the solution :D