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.
| Published in | Pure and Applied Mathematics Journal (Volume 7, Issue 5) |
| DOI | 10.11648/j.pamj.20180705.11 |
| Page(s) | 63-67 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Perfect Number, Odd, Theorem, Number Theory
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APA Style
Renz Chester Rosales Gumaru, Leonida Solivas Casuco, Hernando Lintag Bernal Jr. (2018). Formulating an Odd Perfect Number: An in Depth Case Study. Pure and Applied Mathematics Journal, 7(5), 63-67. https://doi.org/10.11648/j.pamj.20180705.11
ACS Style
Renz Chester Rosales Gumaru; Leonida Solivas Casuco; Hernando Lintag Bernal Jr. Formulating an Odd Perfect Number: An in Depth Case Study. Pure Appl. Math. J. 2018, 7(5), 63-67. doi: 10.11648/j.pamj.20180705.11
AMA Style
Renz Chester Rosales Gumaru, Leonida Solivas Casuco, Hernando Lintag Bernal Jr. Formulating an Odd Perfect Number: An in Depth Case Study. Pure Appl Math J. 2018;7(5):63-67. doi: 10.11648/j.pamj.20180705.11
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Download@article{10.11648/j.pamj.20180705.11,
author = {Renz Chester Rosales Gumaru and Leonida Solivas Casuco and Hernando Lintag Bernal Jr},
title = {Formulating an Odd Perfect Number: An in Depth Case Study},
journal = {Pure and Applied Mathematics Journal},
volume = {7},
number = {5},
pages = {63-67},
doi = {10.11648/j.pamj.20180705.11},
url = {https://doi.org/10.11648/j.pamj.20180705.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180705.11},
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.},
year = {2018}
}
TY - JOUR T1 - Formulating an Odd Perfect Number: An in Depth Case Study AU - Renz Chester Rosales Gumaru AU - Leonida Solivas Casuco AU - Hernando Lintag Bernal Jr Y1 - 2018/11/30 PY - 2018 N1 - https://doi.org/10.11648/j.pamj.20180705.11 DO - 10.11648/j.pamj.20180705.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 63 EP - 67 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20180705.11 AB - 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. VL - 7 IS - 5 ER -
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