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Made available online by the Smarandache Notion Journal and the University of New Mexico - Gallup.
The Smarandache function, say S, is a numerical function defined such that for every positive integer n, its image S(n) is the smallest positive integer whole factorial is divisible by n.
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, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, Romania). 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.
Other new sequences are introduced in number theory, and for each one a general question: how many primes each sequence has.
Prof. univ. dr. Florentin Smarandache este un polivalent om de știință și literat. Pe 10 decembrie 2019 a împlinit 65 ani. Este un savant de factură renascentistă, publicând în foarte multe domenii: matematică (teoria numerelor, statistică, geometrie non-Euclidiană), computere (inteligenţă artificială, fuziunea informaţiei), fizică (fizica cuantică, fizica particulelor), economie (economie culturală, teoria poly-emporium), filosofie (neutrosofie – o generalizare a dialecticii, logica neutrosofică – o generalizare a logicii fuzzy intuiţioniste), literatură (poezie, proză, roman, eseuri, nuvele, drame, teatru pentru copii, traduceri), artă etc.
A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc