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...on, and am(n) denotes the Smarandache m-th power residues function of n. The main purpose of this paper is using the elementary method to study the number of the solutions of the equation (n) = am(n), and give all solutions for this equation....

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...NZHUANG, LIU DUANSEN (EDITORS) RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ... ...BER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005 EDITORS: ZHA... ... SHANGLUO, SHAANXI, P.R.CHINA RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ... ...BER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005... ...ping Ontheintegerpartofthem throotandthe k thpowerfreenumber 41 LiZhanhu 1,2 AFormulaForSmarandacheLCMRatioSequence 45 WangTing Onthem thpowercompleme... ...olutions. §1. Introduction For any positive integer n, let n = p α 1 1 p α 2 2 ···p α k k denotes the factoriza tion ofn into prime powers. The Smara... ...ndachem th power residues function a m (n)aredefinedas a m (n) =p β 1 1 p β 2 2 ···p β k k , β i = min{m−1,α i },i = 1,2.···,k. Inproblem65of[1],Profes... ...at is, weshallprovethefollowing: Theorem. Let m be a fixed integer with m ≥ 2. Then the equation φ(n) =a m (n)havem+1solutions,namely n = 1,2 m ,2 α 3 ... ...e equation φ(n) =a m (n)havem+1solutions,namely n = 1,2 m ,2 α 3 m , α = 1,2,···,m−1. §2. Proofofthetheorem In this section, we shall complete the pro...

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...Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new proble...

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...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WEN... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ... ...ats.htm ISBN : 1 - 931233 - 88 - 8 Standard Address Number : 297 - 5092 Printed in the United States of America This book ... ...ory of Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and... ...se problems, many scholars showed great interests in them (See references [2], [3]). But it seems that no one knows the relationship between these two... ...ormula Taking , in the theorem, we may immediately obtain the following 2 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY Corollary. For any real... ...ER THEORY Corollary. For any real number , we have the asymptotic formula 2. One simple lemma To complete the proof of the theorem, we need the follo... ...dache F. Only problems, not Solutions. Chicago: Xiquan Publ. House, 1993. [2] Liu Hongyan and Zhang Wenpeng. A number theoretic function and its mean ... ...operties of the sequence . About this problem, Professor Zhang and Liu in [2] have studied it and obtained an interesting asymptotic formula. That is,...

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...cu meridianele şi paralelele Volumul II 2 3 ... ...ici te-ajunge la 1.500 $ pe lun ă, iar un apartament cu dou ă camere – la 2.000 $... Keep your eyes open ( Ţine ochii deschi şi!), îmi spune un cet... ...alta cu chilo ţi şi f ăr ă sutien. Cea de-a doua îmi propune s ă pl ătesc 2 $ ca s-o ating cu mâna pe mamele şi 5 $ ca s-o ating în zona vaginal ă.... ...un concert simfonic: Verdi (Uvertura la “Nabucco”), Bizet (“L’Arlesienne 2”), Wagenseil – despre care nu auzisem, Milton L. Bush şi Denza (cu “Fu-n... ...cte distincte trec mai multe drepte! A doua prelegere, “A function in the number theory” (O func ţie în teoria numerelor – “Func ţia Smarandache”!) ... ...em cu ma şina pân ă la poalele muntelui, apoi o lu ăm pe potec ă (trail) 2-3 mile pân ă mai aproape de un baraj. De şertul ăsta! Americanii au tr...

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... another and can be read separately. Findings are illustrated with diagrams and tables. The latter have been kept to a minimum as it is often not the numbers but the general behaviour and pattern of numbers that matters. One of the facinations with number problems is that they are often easy to formulate but hard to solve – if ever, and if one finds a solution, new questio...

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...l Numbers - a few elementary studies on Smarandache sequences and other number problems Henry Ibstedt American Research Press Reho... ... The surprising behaviour of a sequence Mainly Natural Numbers - a few elementary studies on Smarandache sequences and other... ...t form loops and has no terminating value. Its definition is simply a 1 =a 2 =1, a 2k+1 =a k+1 -1, a 2k+2 =a k+1 +1 This book can be ordered in... ...randache/eBooks-otherformats.htm ISBN: 1-931233-73-X Standard Address Number: 297-5092 Printed in the United States of America 3 ... ...s and tables. The latter have been kept to a minimum as it is often not the numbers but the general behaviour and pattern of numbers that matters. O... ... x n =(1 +x 0 +x 1 + …x n-1 )/n with x 0 =1 produce natural numbers for n=1,2, … 42 but not for n= 43. An explanation to this was given by the autho... ...ache partial perfect additive sequence has a very simple definition: a 1 =a 2 =1, a 2k+1 =a k+1 -1, a 2k+2 =a k+1 +1. It does not form loops and it ... ... types of relations leads to the conclusion that there are infinitely many 2-2 additive relations and that k-k relations exist for large values of ... .... An interesting observation is the great involvement of prime twins in the 2-2 relations. Chapter VIII. An analysis of the number of relations ...

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...This book contains 23 papers, most of which were written by participants to the fifth International Conference on Number Theory and Smarandache Notions held in Shangluo University, China, in March, 2009. In this Conference, several professors gave a talk on Smarandache Notions and many participants lectured on them both extensively and i...

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...3. Remarks Sandor [2] has considered the problem of finding the S-perfect and completely S-perfect numbers, but his proof is not complete. He has proved that the only S-perfect of the form n = p q is n = 6 and there is no S-perfect number of th...

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...Cheng : An equation involving the Smarandache double factorial function and Euler function 8 A. A. K. Majumdar : S-perfect and completely S-perfect numbers 12 B. Zhao and S. Wang: Cyclic dualizing elements in Girard quantales 21 P. Chun and Y. Zhao : On an equation involving the Smarandache function and the Dirichlet divisor function 27 F. Li and Y. Wang : An equatio...

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...CONTENTS 1. Foreword 2. General information 3. Definitions of terms used 4. Usage reports 5. Data processing 6. Auditing 7. Compliance 8. References to other standards, protocols and codes of practice 9. Governance of COUNTER 10.Maintena...

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...ctice Books and Reference Works Release 1: March 2006 CONTENTS 1. Foreword 2. General information 3. Definitions of terms used 4. Usage reports 5. D... ... 10.Maintenance and development of the COUNTER Code of Practices Appendices 2 Note: Sections 3, 4, and 5 contain the core information required for im... ...orked Electronic Resources) was formally established in March 2002. Release 2 of the COUNTER Code of Practice for Journals and Databases was published... ... & Francis Group Thieme Publishing Group UKSG, United Kingdom Serials Group 2. General information 2.1Purpose The purpose of the COUNTER Codes of Prac... ...tatistics that are consistent, credible and compatible. COUNTER builds on a number of important ongoing initiatives, standards and protocols, See Sect... ...mportant ongoing initiatives, standards and protocols, See Section 8 below. 2.2Scope This COUNTER Code of Practice provides a framework for the record... ...ter Online Metrics, a not­for­profit company registered in England (Company Number 4865179). Counter Online Metrics is governed by a Board of Director... ...rom the communities it serves. Each new version will be made available as a numbered Release on the COUNTER website and users will be alerted to its a... ...her standards, protocols and codes The COUNTER Codes of Practice build on a number of existing industry initiatives and standards that address vendor­...

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...described in this book are based traditional tables games which have been modified to fit into a fantasy world where the inhabitants use a duodecimal numbering system (Base 12), and for whom the hexagon and numbers which are multiples 6 are of fundamental importance. When developing these table games the aim was to produce games with simple rules (easy to learn) which l...

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...gdoms of Westron, Stron, and Eastron. The purpose of this book (Volume 1) is to define the rules of the Elstron Table Games. A second book (Volume 2) will describe how these games evolved, including the games they were developed from and the sources used, along with the story of their historical development and cultural importance within the Elstron Kingdoms. The app...

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... The Businessman 44 The Janitor 45 Shy Attack 46 The Fisherman Views Creation 48 The Drunkard Views Creation 49 Street Scene 50 Still Life 52 Numbers 53 Words 54 Janet 56 Richard Bradley 57 Weather-Beaten and Truth-Seasoned 58 What to Say to the Next Messiah on Your Doorstep or TV 60 Moses 61 The Murderer’s Confession 63 For Us (With Love) 65 Prayer of the...

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...iscoveries made over last 30 or so years shed some new and important light on many events in that history. These discoveries have been published in a number of books and scholarly papers. For those who do not have time, or inclination to go over those numerous sources, this short (intentionally short) book retells the early history of the Jewish people in light of those di...

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...Introduction 1. People, Place and Time 2. First Humans. 3. Semites in Canaan 4. Israel emerges in Canaan 5. Who were the early Israelites? ‘ 6. From tribes to people 7. Nation Formed: the Jewish States Epilogue References ...

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...esearch Press Rehoboth, NM 2002 A 11 L A 7 A 8 A 6 A 10 A 1 A 2 A 3 A 4 A 5 2 The picture on the cover represents the lattice... ...lup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-63-2 Standard Address Number: 297-5092 PRINTED IN THE UNITED STATES OF AME... ...he/eBooks-otherformats.htm ISBN: 1-931233-63-2 Standard Address Number: 297-5092 PRINTED IN THE UNITED STATES OF AMERICA 3 CONTENTS ... ... 5 1. General Fundamentals 1.1 Basic Concepts 7 1.2 A few properties of groups and graphs 8 1.3 Lattices and its properti... ...es of groups and graphs 8 1.3 Lattices and its properties 11 2. Loops and its properties 2.1 Definition of loop and examples 1... ... Loops and its properties 2.1 Definition of loop and examples 15 2.2 Substructures in loops 17 2.3 Special identities in loops 22... ...kground in algebra and more specifically a strong foundation in loops and number theory. 6 This book introduces over 75 Smarandache concept... ...the introduction of a new class of loops of even order. We prove that the number of different representations of right alternative loop of even orde... ...n order (2n), in which square of each element is identity is equal to the number of distinct proper (2n – 1) edge colourings of the complete graph K...

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... = arcsin(v)} S' a b f 1 v a / b σ σ σ σ e a 1 cos(θ θ θ θ) (4) cos 2 (θ θ θ θ) (4) sin(θ θ θ θ)cos(θ θ θ θ) (5.1) a 2 sec(θ θ θ θ) (4... ...(5.1) a 2 sec(θ θ θ θ) (4) 1 (4) tan(θ θ θ θ) (5.1) sin(θ θ θ θ) (2) sec(θ θ θ θ) (3.1) sec (θ θ θ θ) [1 - v cos (Φ Φ Φ Φ)] (9.5) ... ... American Research Press Rehoboth 2001 2 L. Stephen Young G-DIMENSIONAL THEORY & THE SMARANDACHE QUANT... ...ords 4 1 . I n t r o d u c t i o n 4 - 5 2. The Smarandache Quantum Paradoxes 5-8 3 . G D T R e l a t i v i ... ...Quantum Paradoxes 5-8 3 . G D T R e l a t i v i t y 8 - 2 0 4 . G D T P a r t i c l e F i e l d s 2 0 - 3 2 5. The... ...unm.edu/~smarandache/physics.htm ISBN: 1-931233-46-2 Standard Address Number 297-5092 Printed in the United States of America 4 G-... ...ht seem due solely to semantic vagueness in defining the maximum or minimum number of wheat grains constituting a "heap", however, as noted in the St... ...le quantum states (on/off); yet the computer as a whole has a near-infinite number of possible states. This then serves an example of apparent non- p... ... ruled out when we consider the on/off switch. The computer's near-infinite number of states can be logically reduced to two states: on and off. thus...

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...The new single is atom made up of two sub atomic particle rings, each ring comprising a number of energy nodes. If we look at the atom in detail we see it has a vortex pressure map giving the atom a small graviton pull. These forces are built up from the two vortex forces of the two particles rings which are loc...

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...FORMATION OF COMPLEX ATOMS In this book- 1 Formation of Complex Atoms - 2 Elemental Bonding - 3 Core to Core Bonding - 4 Structure of Complex Atoms - 5 Building the Atomic Core Stack...

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...When Rashad Khalifa proclaimed that he has discovered a mathematical code of Quran, which is number "19" even though most of the Islamic Scholars where awaiting to see how he is going to react next but still some very few scholars ignored the crucial command, guideline of Al-Quran given below and the evil consequence...

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...see, what the other Israelites were unable to see. Khalifa: Proclaimed that he was able to see [19], what the other Muslims were unable to see. 2) Saamri: Took a handful (of dust) from the footprint of the Messenger, and threw it (into the calf). Thus did his soul suggested to him. Khalifa: Took a hint from the footprint (History) of the Messenger [See Khalifa's A...

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...1) Editorial NOTES 2) Preface 3) Chapter-1 Introduction 4) Chapter-2 Historical background of the work of Khalifa 5) Chapter-3 Khalifa’s Hadiths 6) Chapter-4 Khalifa’s Claim Of Messenger-ship 7) Chapter-5 Crazy cl...

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...009 © debtconsolidationcare.com 1 INDEX Srl Topic Page 1 Acknowledgements 4 2 About Debtconsolidationcare.com 5 3 Contact Credit Companies 6 4... ...tter with alternate Payment Strategy 26 2005-2009 © debtconsolidationcare.com 2 22 Acceptance of verbal offer for Debt Settlement 27 23 Debt Sett... ...your credit database. Your Full Name: Your Birth Date: Your Social Security Number: Your Current address: Your Former address: I have enclos... ...laims. I would also like to request for the business names, addresses and phone numbers of the people who have been contacted for the process. This ... ...reinvestigation and verification processes. Name of the Creditor/agency/account number: Here, state the reasons for disputing this negative mark. Si... ...he agreement which authorizes the creditor to collect debt on the alleged debt. 2. The signed agreement from the debtor conforming to pay the credito... ...itor name, date of inquiry, reason why the inquiry should be removed: older than 2 years, unauthorized, other). There are errors in my personal da... ...effect. Sincerely, Your name your address your home and office phone number your social security number Back to Index 2005-2009 ©... ...009 © debtconsolidationcare.com 22 Unsolicited offer to the Creditor Example 2 If you want to go ahead and make a creditor a written offer with...

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...Language is used to express ideas. A Sentence is the full expression of a single idea. A Language is learned by memorizing a number of Sentences and acquiring a vocabulary of some hundreds of words. Now, since a Sentence is composed of words, and words are “parts off speech,” and their proper arrangement constitutes a Sentence, Grammar must be inc...

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...The Adjective. Classification. Comparison. Adjective as a Noun, and the Noun as an Adjective. Participles -- 22-23 -- Lesson 4 -The Noun, Gender, Number, Case. Declension. Syntax -- 23-26 -- Lesson 5 - The Personal Pronoun. Table of. Declension -- 27-31 -- Lesson 6 - Demonstrative, Interrogative, and Indefinite Pronouns, and Adjective Pronouns -- 31-32 -- Lesson 7 ...

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...D BOOKS OF THE EAST SERIES IN 50 VOLUMES Vols. r, 15. THE UPANI~ADS, in 2 vols. : F. Max Miiller. 2, 14. THE SACRED LAWS OF THE ARYAS, in 2 vols.:... ... 24, 37, 47. PAHLAVI TEXTS, in 5 vols. : E. W. West. 6, g. THE QUR'AN, in 2 vols. : E. H. Palmer. 7. THE INSTITUTES OF VI~~U : Julius J olly. S. TH... ...ds & H ermann Oldenberg. . 19· THE FO-SHO-HING-TSAN-KING : Samuel Beal. 2 r. THE SADDHARMA-PU~OARIKA or The Lotus of the True Law: H. Kern. 22, 4... ...U~OARIKA or The Lotus of the True Law: H. Kern. 22, 45. JAINA SUTRAS, in 2 vols. : Hermann J acobi. , 25 . MANU: Georg Biihler. 29, 3 0 . THE GB-... ...n J acobi. , 25 . MANU: Georg Biihler. 29, 3 0 . THE GB-IHYA-SUTRAS, in 2 vols. : Hermann Oldenberg & F. Max Milller. 3 2 , 46 . VEDIC HYMNS, in ... ...s, and the smaller roman pages of the Introductions. 1 Where a very large number of references arc given, some references have been italicized to po... ...t ont the more important passages. 2 But after a figure, referring to the number of page, ~ note, and after a Sanskrit term = neuter. LIST OF THE 4...

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...........................................................................3 2.The essence of data recovery ............................................... ...........................................................................4 2.Hardware reason ............................................................ ...........................................................................6 2.SPS......................................................................... ...........................................................................8 2.Main technical specification and parameter of hard disk..................... ..........................................................................16 2.Advanced formatting of hard disk............................................ ... of the array is equal to the MTBF of an individual drive, divided by the number of drives in the array. Because of this, the MTBF of a non-redundan... ...tion to amount of data that a server can access, currently limited by the number of storage devices, which can be attached to the individual server... ...it board and interface parts. A hard disk is a sealed unit containing a number of platters in a stack. Hard disks may be mounted in a horizontal o... ...ure, and are established when the disk is low-level formatted. Tracks are numbered, starting at 0 (the outermost edge of the disk), and going up to ...

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...........................................................................3 2.The essence of data recovery ............................................... ...........................................................................4 2.Hardware reason ............................................................ ...........................................................................6 2.SPS......................................................................... ...........................................................................8 2.Main technical specification and parameter of hard disk..................... ..........................................................................16 2.Advanced formatting of hard disk............................................ ... of the array is equal to the MTBF of an individual drive, divided by the number of drives in the array. Because of this, the MTBF of a non-redundan... ...tion to amount of data that a server can access, currently limited by the number of storage devices, which can be attached to the individual server... ...it board and interface parts. A hard disk is a sealed unit containing a number of platters in a stack. Hard disks may be mounted in a horizontal o... ...ure, and are established when the disk is low-level formatted. Tracks are numbered, starting at 0 (the outermost edge of the disk), and going up to ...

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...CONTENTS Ch. No. TITLE PAGE No. 1. BIOCHEMISTRY-Scope and Importance in Medical Sciences 1-2 2. GENERAL CHEMISTRY 3-10 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Water Acids And Bases pH Buffers Colloids Osmosis Radioactivity 5 5 6 6 8 8 9 3. CELL -Structure and Function 11-13 4. CARBOHYDRATES 14-24 4.1 4.2...