number theory

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21: Peter Paule

… ►Paule’s main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. …

… ►Walker’s published work has been mainly in real and complex analysis, with excursions into analytic number theory and geometry, the latter in collaboration with Professor Mowaffaq Hajja of the University of Jordan. …

23: 27.5 Inversion Formulas

… ►Special cases of Möbius inversion pairs are: … ►Other types of Möbius inversion formulas include: …

24: 27.3 Multiplicative Properties

§27.3 Multiplicative Properties

… ►

27.3.8

\phi\left(m\right)\phi\left(n\right)=\phi\left(mn\right)\phi\left(\left(m,n% \right)\right)/\left(m,n\right).

ⓘ

Symbols:: $\phi\left(\NVar{n}\right)$ : Euler’s totient, $\left(\NVar{m},\NVar{n}\right)$ : greatest common divisor (gcd), $m$ : positive integer and $n$ : positive integer
Permalink:: http://dlmf.nist.gov/27.3.E8
Encodings:: pMML, png, TeX
See also:: Annotations for §27.3 and Ch.27

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25: 27.16 Cryptography

… ►Thus,

y\equiv x^{r}\pmod{n}

and

1\leq y<n

. …

26: Tom M. Apostol

… ►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. … ►

27 Functions of Number Theory

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27: 27.22 Software

… ►

•

Number Theory Web. References and links to software for factorization and primality testing.

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28: Mourad E. H. Ismail

… ► Suslov), Kluwer Academic Publishers, 2001; Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (with F. …

29: Morris Newman

… ►He served as Associate Editor for Combinatorics and Number Theory for the DLMF project. …

30: 27.12 Asymptotic Formulas: Primes

… ►The largest known prime (2018) is the Mersenne prime

2^{82,589,933}-1

. … ►Descriptions and comparisons of pseudoprime tests are given in Bressoud and Wagon (2000, §§2.4, 4.2, and 8.2) and Crandall and Pomerance (2005, §§3.4–3.6). … ►