17. A positive integer is called perfect provided the sum of its proper positive divisors is . For example, 6 is perfect because 6 =1+2+3. Another perfect number is 496. Indeed, 496 = 31 . 16, and we see that the positive proper divisors of 496 are 1, 2, 4, 8, 16, 31, 31 . 2 = 62, 31 . 4 = 124, 31 . 8 = 248. Then we add them up and get 1 + 2+ 4+ 8+ 16 + 31 + 62 + 124 + 248 = 496. If we include r as divisor of itself, we see that x is perfect if and only if the sum of all of its positive divisors (including x) is 2r. A number of the type 2" - 1 is sometimes a prime, then called a Mersenne prime. If 2" - 1 is a prime, show that r = 2"-1(2" - 1) is a perfect number. Hint. You should be able to see a pattern in the factors of r and also to add them up. Don't forget that 2" - 1 is given to be prime