Pure and Applied Mathematics Journal

Archive

Volume 7, Issue 5, October 2018

  • Formulating an Odd Perfect Number: An in Depth Case Study

    Renz Chester Rosales Gumaru, Leonida Solivas Casuco, Hernando Lintag Bernal Jr

    Issue: Volume 7, Issue 5, October 2018
    Pages: 63-67
    Received: 17 September 2018
    Accepted: 29 October 2018
    Published: 30 November 2018
    DOI: 10.11648/j.pamj.20180705.11
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    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 ... Show More
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  • Proving the Collatz Conjecture with Binaries Numbers

    Olinto de Oliveira Santos

    Issue: Volume 7, Issue 5, October 2018
    Pages: 68-77
    Received: 13 October 2018
    Accepted: 22 November 2018
    Published: 24 December 2018
    DOI: 10.11648/j.pamj.20180705.12
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    Abstract: The objective of this article is to demonstrate the Collatz Conjecture through the Sets and Binary Numbers Theory, in this manner: 2n + 2n-1+...1. This study shows that there are subsequences of odd numbers within the Collatz sequences, and that by proving the proposition is true for these subsequences, it is subsequently proven that the entire pro... Show More
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