Prime Factorization of Sums and Differences of Two Like Powers

Rafał Ziobro. "Prime Factorization of Sums and Differences of Two Like Powers." Formalized Mathematics 24.3 (2016): 187-198. <http://eudml.org/doc/288046>.

@article{RafałZiobro2016,
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].},
author = {Rafał Ziobro},
journal = {Formalized Mathematics},
keywords = {integers; factorization; primes},
language = {eng},
number = {3},
pages = {187-198},
title = {Prime Factorization of Sums and Differences of Two Like Powers},
url = {http://eudml.org/doc/288046},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Rafał Ziobro
TI - Prime Factorization of Sums and Differences of Two Like Powers
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 3
SP - 187
EP - 198
AB - 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].
LA - eng
KW - integers; factorization; primes
UR - http://eudml.org/doc/288046
ER -