MathDB

Let A \equal{} \{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) \minus{} N(1) \plus{} N(2) \minus{} N(3) \plus{} N(4) \minus{} N(5) \plus{} N(6)\minus{}N(7) \equal{} 0 EDITED : thx for cosinator.. BTW, your statement and my correction give 80% hint of the solution :D

Problem Statement