2008 Indonesia MO Problems/Problem 4

Problem

Note: Problem statement slightly modified for correction.

Let $A = \{1,2,\ldots,2008\}$ .

(a) Find the number of subset of $A$ such that the product of its elements is divisible by 7.

(b) Let $N(i)$ denotes the number of subset of $A$ in which the sum of its elements, when divided by 7, leaves the remainder $i$ . Prove that $N(1) - N(2) + N(3) - N(4) + N(5) - N(6) = 0$ .

2008 Indonesia MO (Problems)
Preceded by Problem 3	1 • 2 • 3 • 4 • 5 • 6 • 7 • 8	Followed by Problem 5
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2008 Indonesia MO Problems/Problem 4

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