Various Arithmetic Functions and their Applications

Authors

Florentin Smarandache, University of New MexicoFollow
Octavian Cira

Document Type

Book

Publication Date

2016

Abstract

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, University of Craiova Library, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, România). The book is based on various articles in the theory of numbers (starting from 1975), updated many times.

Special thanks to C. Dumitrescu and V. Seleacufrom the University of Craiova (see their edited book "Some Notions and Questions in Number Theory", Erhus Press, Glendale, 1994), M. Bencze, L. Tutescu, E. Burton, M. Coman, F. Russo, H. Ibstedt, C. Ashbacher, S. M. Ruiz, J. Sandor, G. Policarp, V. Iovan, N. Ivaschescu, etc. who helped incollecting and editing this material.
This book was born from the collaboration of the two authors, which started in 2013. The first common work was the volume "Solving Diophantine Equations", published in 2014. The contribution of the authors can be summarized as follows: Florentin Smarandache came with his extraordinary ability to propose new areas of study in number theory, and Octavian Cira – with his algorithmic thinking and knowledge of Mathcad.

Publisher

Pons Asbl, Brussels

ISSN

978-1-59973-372-2

Language (ISO)

English

Keywords

sequences, integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes

Recommended Citation

Smarandache, Florentin and Octavian Cira. "Various Arithmetic Functions and their Applications." (2016). https://digitalrepository.unm.edu/math_fsp/256

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.