Confirm
Archive
Special Issues
Formulating an Odd Perfect Number: An in Depth Case Study
Pure and Applied Mathematics Journal
Volume 7, Issue 5, October 2018, Pages: 63-67
Received: Sep. 17, 2018; Accepted: Oct. 29, 2018; Published: Nov. 30, 2018
Authors
Renz Chester Rosales Gumaru, Senior High School Department, Arellano University, Pasay, Philippines
Leonida Solivas Casuco, Senior High School Department, Norzagaray National High School, Norzagaray, Philippines
Hernando Lintag Bernal Jr, General Education Department, Far Eastern University – NRMF, Fairview Quezon City, Philippines
Article Tools
Abstract
A perfect number is a positive integer that is equals to the sum of its proper divisors. No one has ever found an odd perfect number in the field of Number Theory. This paper review discussed the history and the origin of Odd Perfect Numbers. The theorems and proofs are given and stated. This paper states the necessary conditions for the existence of odd perfect numbers. In addition, several related studies such as “Odd Near-Perfect Numbers” and “Deficient-Perfect Numbers”. Formulating odd perfect numbers will have a significant contribution to other Mathematics conjectures. This paper compiles all the known information about the existence of an odd perfect number It also lists and explains the necessary theorems and lemmas needed for the study. The results and conclusions shows the ff: Odd Perfect Numbers has a lower bound of 101500, The total number of prime factors/divisors of an odd perfect number is at least 101, and 108 is an appropriate lower bound for the largest prime factor of an odd perfect number and the second large stand third largest prime divisors must exceed 10000 and100 respectively. In summary, it found out that there is a chance for an odd perfect number to exist even if there is a very small possibility.
Keywords
Perfect Number, Odd, Theorem, Number Theory
Renz Chester Rosales Gumaru, Leonida Solivas Casuco, Hernando Lintag Bernal Jr, Formulating an Odd Perfect Number: An in Depth Case Study, Pure and Applied Mathematics Journal. Vol. 7, No. 5, 2018, pp. 63-67. doi: 10.11648/j.pamj.20180705.11
References
[1]
[2]
[3]
Bogomolny, Alexander. (2017) Pythagorean Triples and Perfect Numbers.
[4]
[5]
Caldwell, Chris K. (2016). Mersenne Primes: History, Theorems and Lists. Retrieved from https://primes.utm.edu/mersenne/.
[6]
Brown, D. R. (2011). "Odd Perfect Numbers".
[7]
Carr, Aver. (2013). "Odd Perfect Numbers: Do They Exist?"
[8]
[9]
[10]
[11]
What is the difference between a research paper and review paper. (2015). Retrieved from https://www.editage.com/insights/what-is-the-difference-between-a-research-paper-and-a-review-paper.
[12]
[13]
Stevens, Ben. (2012). A Study on Necessary Conditions for Odd Perfect Numbers”.
[14]
Adajar, Carlo. (2016, University of the Philippines Diliman), On Odd Near-Perfect and Deficient- Perfect Numbers.
[15]