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Prime Factorization of Sums and Differences of Two Like Powers

100%

Ziobro R.

Formalized Mathematics

2016

tom 24

nr 3

187-198

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].

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

100%

Ziobro R.

Formalized Mathematics

2015

tom 23

nr 3

215-229

Solving equations in integers is an important part of the number theory [29]. In many cases it can be conducted by the factorization of equation’s elements, such as the Newton’s binomial. The article introduces several simple formulas, which may facilitate this process. Some of them are taken from relevant books [28], [14]. In the second section of the article, Fermat’s Little Theorem is proved in a classical way, on the basis of divisibility of Newton’s binomial. Although slightly redundant in its content (another proof of the theorem has earlier been included in [12]), the article provides a good example, how the application of registrations could shorten the length of Mizar proofs [9], [17].

Problems and results on αp - βq

88%

Ramachandra K., Sankaranarayanan A., Srinivas K.

Acta Arithmetica

1996

tom 75

nr 2

119-131

Ograniczanie wyników

2 Formalized Mathematics

1 Acta Arithmetica

2 Ziobro R.

1 Ramachandra K.

1 Sankaranarayanan A.

1 Srinivas K.

1 2016

1 2015

1 1996

Wyniki wyszukiwania

Prime Factorization of Sums and Differences of Two Like Powers

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

Problems and results on αp - βq