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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 24, Issue 3 (Sep 2016)


Prime Factorization of Sums and Differences of Two Like Powers

Rafał Ziobro
  • Department of Carbohydrate Technology University of Agriculture Krakow, Poland
Published Online: 2017-02-21 | DOI: https://doi.org/10.1515/forma-2016-0015


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].

MSC: 11A51; 03B35

Keywords: integers; factorization; primes

MML: identifier: NEWTON03; version: 8.1.05 5.37.1275


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About the article

Received: 2016-06-30

Published Online: 2017-02-21

Published in Print: 2016-09-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2016-0015.

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© by Rafał Ziobro. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License BY-SA 3.0 LEGALCODE

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