User talk:Vachagan

All perfect numbers are even ։ Divisors theorem

This page is about all Perfect numbers are even, and there is no odd perfect number.

Theorem

Nicomachus of Gerasa bring following theorems

1. The ${\ n ^ {th}}$ perfect number has n digits. This was false
2. All perfect numbers are even. Not confirmed
3. All perfect numbers ending 6 and 8 alternately. This was false
4. Euclid's algorithm produces every even perfect number. This is true
5. There are infinitely many perfect numbers. Not confirmed

Proof: All perfect numbers are even.

${\ N}$ perfect number can't be odd. Let me explain why. We know simple thing that perfect number have divisiors which sum is equal to itself.

${N = \sum_{i=1}^{n}(d_i)}$