If p and q are distinct prime numbers prove n pq is a produ

If p and q are distinct prime numbers, prove n = pq is a product perfect number.

Solution

Perfect number, a positive integer that is equal to the sum of its proper divisors [except itself]. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.

Every integer can be uniquely expressed as the product of prime numbers .

considering a perfect number 6 , 6 = 2x3,a product of two distinct prime numbers 2 and 3.

If n is a perfect number, it can be expressed as a product of power of a prime number \'p\' and a prime number \'q\' .

For example, if n= 28, 28 =4x7 = 2² x7

n=496, 496= 16x31 = 2⁴x31

Hence proved.