On the Euler’s Form of an odd Perfect Number

Abstract

Euler has proved that an odd perfect number, if exists, must be of the form ... , ≡ ≡ 1 (mod 4). In this article, we show: (i) An alternative proof to the Euler’s form of odd perfect numbers. (ii) An odd number of the form: , ≡ ≡ 1 (mod 4) cannot be perfect.