I've done that (just summing all the listed proper divisors and checking ).Euclid’s theorem about perfect numbers* depends on the prime divisor property, which will be proved in the next exercise.
Assuming this for the moment, it follows that if is a prime ,
then the proper divisors of are and .
Given that the divisors of are those just listed, show that is perfect when is prime.
* That if is prime, then is perfect.
Help with this one.We can now fill the gap in the proof of Euclid’s theorem on perfect numbers* (above exercise), using the prime divisor property.
Use the prime divisor property* to show that the proper divisors of , for any odd prime , are and .
* If is a prime that divides , then divides or .