<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases).</p><p>Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization, which could serve in further development of Mizar projects [2]. This could be regarded as one of the important benefits of proof formalization [9].</p></abstract>

Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases).Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization, which could serve in further development of Mizar projects [2]. This could be regarded as one of the important benefits of proof formalization [9].

Prime Factorization of Sums and Differences of Two Like Powers

Department of Carbohydrate Technology University of Agriculture Krakow,

Formalized Mathematics

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

{"article-title":"Prime Factorization of Sums and Differences of Two Like Powers"}

Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4],...

Prime Factorization of Sums and Differences of Two Like Powers

Published Online: Feb 21, 2017

Page range: 187 - 198

Received: Jun 30, 2016

DOI: https://doi.org/10.1515/forma-2016-0015

Keywords
integers, factorization, primes

© by Rafał Ziobro

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

Prime Factorization of Sums and Differences of Two Like Powers

Published Online: Feb 21, 2017

Page range: 187 - 198

Received: Jun 30, 2016

DOI: https://doi.org/10.1515/forma-2016-0015

Keywordsintegers, factorization, primes

© by Rafał Ziobro

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

Keywords
integers, factorization, primes