Proof of Non-existence of odd Perfect Numbers

P. Vivekanand

Maths IIT and Olympiad Faculty Raman High School, Subedari, Hanamkonda,

Warangal District. E-mail:


            An odd perfect number is a number whose sum of factors is equal to double the number it self and the number is odd. The existence or non- existence is not known since the time of Euclid. With some basic results found in internet the author proves the theorem. The results used from internet are mentioned in the proof. It has been 2000 years since the problem is posed and unsolved. So let us go into the proof. We have used Egyptian fractions and had obtained only a single page proof. It stresses the importance of Egyptian fractions in number theory.





International eJournal of Mathematical Sciences, Technology and Humanities

Volume 4, Issue 3, Pages:  1349 - 1354