Euler did not prove it, Euiclid did.

The important fact that the sum of divisors number-theortic function is weakely multiplicative.

That is if then,

The prove is simple because,

Since is multiplicative so that is .

What is where ?

Since is odd and only have even divisors we have,

Thus,

Now,

is a Mersenne prime thus,

And,

That is a geometric series whose sum is,

Thus,

Thus,

is perfect.

(The converse that an even perfect number has this form is a little bit more complicated).

Q.E.D.