MathDB

We say a natural number

n

is perfect if the sum of all the positive divisors of

n

is equal to

2n

. For example,

6

is perfect since its positive divisors

1,2,3,6

add up to

12=2\times 6

. Show that an odd perfect number has at least

3

distinct prime divisors.
Note: It is still not known whether odd perfect numbers exist. So assume such a number is there and prove the result.

Problem Statement