An integer n is called a perfect number if it equals the sum of all of its positive divisors (excluding itself). For example, 28 is perfect as the divisors of 28 are 1, 2, 4, 7, 14 and 28, and 1 + 2 + 4 + 7 + 14 = 28. Show that if (2^p) − 1 is a prime number, then (2^(p−1))*((2^p) − 1) is a perfect number.
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