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This volume teaches you children's basic arithmetic in Hawaiian.

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...well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedrons. Other t...

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...József Sándor GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS ***********************************... ... CLUJ-NAPOCA, ROMANIA Geometric Theorems, Diophantine Equations, and Arithmetic Functions ... ...e United States of America "...It is just this, which gives the higher arithmetic that magical charm which has made it the favourite science of th... ...eatly surpasses other parts of mathematics..." (K.F. Gauss, Disquisitiones arithmeticae, G ottingen, 1801) 1 Preface This book contains short notes ... ...is divided into ve chapters: Geometric the- orems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and... ...the remarkable elements of triangles or tetrahedrons. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Ch... ...ions. Article 20 may be considered also as an introduction to Chapter 3 on Arithmetic functions. Here many papers study the famous Smarandache functio... ...or analogues functions. Other topics are connected to the com- position of arithmetic functions, arithmetic functions at factorials, Dedekind’s or Pil... ...es, III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 12 An arithmetic problem in geometry . . . . . . . . . . . . . . . . . . . . . . ...

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...enclosure, for some of the problems are not so new and creative. But reading carefully, there are also some problems which stimulate the curiosity on arithmetic functions and number sequences. Then I needed almost no time to understand his talent in mathematics. I returned a letter to the student with a copy of my publication in The Mathematical Scientist and including a r...

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...Jozsef Sandor ON ADDITIVE ANALOGUES OF CERTAIN ARITHMETIC FUNCTIONS 29-32 M. Perez (Ed.) ON SOME SMARANDACHE PROBLEMS 33-38 M. Perez (Ed.) ON SOME PROBLEMS RELATED TO SMARANDACHE NOTIONS 39-40 G. Gregory (Ed.) GENERALIZED SMARANDACHE PALINDROME 41 M. Vassilev - lVl...

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...main purpose is to introduce some of the research of Smarandache problems to readers, comprehensively and systematically, including the mean value of arithmetic functions, identities and inequalities, infinite series, the solutions of special equations, and put forward to some new interesting problems. We hope that the readers could be interested in these issues. At the ...

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...randache Sequence of Unhappy Numbers 37 Muneer Jebreel Karama On m -th power free part of an integer 39 Zhao Xiaopeng and Ren Zhibin On two new arithmetic functions and the k -power complement number sequences 43 Xu Zhefeng Smarandache Replicating Digital Function Numbers 49 Jason Earls On the m -power residues numbers sequence 53 Ma Yuankui , Zhang Tianping ...

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...e, who listed many new and unsolved problems in number theory. Preface Arithmetic is where numbers run across your mind looking for the answer. A... ...nsofthe equationφ(n) = am(n),andgiveallsolutionsforthisequation. Keywords: Arithmeticalfunction;Equation;Solutions. §1. Introduction For any positive ... ...nctionφ(n),andgiveaninteresting identity. Keywords: Multiplicativefunction;Arithmeticalproperty;Identity. §1. Introduction For any positive integern≥ ... ...fδ k (n)byϕ(n),andfindallthensuchthatϕ(n)| δ k (n). Keywords: Eulerfunction;Arithmeticalfunction;Divisibility. §1. Introductionandmainresults For a fixe... ...s For a fixed positive integer k and any positive integer n, we define a new arithmeticfunctionasfollowing: δ k (n) = max{d|d|n,(d,k) = 1} If n ≥ 1 the ... ...1 k +O x 2− 2 k . For any fixed positive integerm, the definition of the arithmetical function δ m (n)is δ m (n) = max{d∈N | d|n,(d,m) = 1}, if n6... ...mentary and analytic methods to study the mean value properties of the new arithmetical function δ m (a k (n)), and give ∗ ThisworkissupportedbyN.S.F.... ...estheproofofLemma1. Lemma 2. For any real number x ≥ 3 and any nonnegative arithmetical functionf(n)withf(0) = 0,wehavetheasymptoticformula: X n≤x f(a... ...eresting identity involving the hexagon numbers. Keywords: Hexagon number;Arithmeticalproperty;Identity. §1. Introduction Foranypositiveintegerm,ifn ...

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...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. ... ...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente...

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... Any function whose domain is some subset of set of integers is called an arithmetic function. DEFINITION 1.1.4: An arithmetic function f(n) is sa... ...native laws left, 20 right, 20 Anti-symmetric, 11 ARIF-loop, 50, 72 Arithmetic function, 8 Associative loop, 22, 35 Associative triple, 26, ...

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...ligious education was the more for­ mal education of reading, writing, and arithmetic. Many of the black parents in the South did not have the opport...

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...is absent there is no circumference at all. That is pure and simple basic arithmetic. This point has no continuity. It comes into being in response t...

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...he prophets were t aught the future by means of these emblems, as a blind man is taught arithmetic by means of counters. They never speak in the spi...

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...X. Pan and B. Liu : On the irrational root sieve sequence 1 H. Liu : Sub-self-conformal sets 4 K. Liu : On mean values of an arithmetic function 12 L. Wang and Y. Liu : On an infinite series related to Hexagon-numbers 16 X. Ren, etc. : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebr...

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...66 6 Simple-Level Logic • Type casting…………………………………………………...77 • Local variables………………………………………….…….78 • Simple operations…………………………………………..82 • Arithmetic operators……………………………….……..83 75 7 Moderate-Level Logic • Relation operators……………………………………..….091 • Equality operators………………………………….………091 • Conditional operators……………………………….…..091 • packaging…………………………………………...

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...at are mathematics articles about concepts and research related to Romanian scientist, Florentin Smarandache, such as semigroups, rings not partners, arithmetic functions, and Smarandache conjectures or problems etc.. The book can be downloaded from the site. ...

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...INSULA 74 THE ROMAN NUMERALS 74 THE ARABIC/HINDU NUMBERS AND OUR DECIMAL SYSTEM 75 THE ORIGIN OF THE BRANCHES OF MATHEMATICS 76 THE ORIGIN OF ARITHMETIC 76 THE ORIGIN OF GEOMETRY 76 THE ORIGIN OF TRIGONOMETRY 77 THE ORIGIN OF ALGEBRA 78 THE ORIGIN OF ANALYTIC GEOMETRY 78 THE ORIGIN OF CALCULUS 79 THE PROPERTIES OF THE DIFFERENT MATHEMATICAL SCIENCES ...