Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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10006 - Beihang Univ. (BUAA) 10007 - Beijing Institute of Technology 10008 - Univ. of Science and Technology Beijing 10010 - Beijing Univ. of Chemical Tech. 10013 - Beijing Univ. of Posts and Telecommunications 10019 - China Agricultural Univ (CAU) 10022 - Beijing Forestry Univ. 10026 - Beijing University of Chinese Medicine 10027 - Beijing Normal Univ. 10028 - Capital Normal Univ. 10029 - Capital Institute of Physical Educations 10030 - Beijing Foreign Studies University 10031 - Beijing International
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------------------------------------------------- 1 (number) 1 | −1 0 1 2 3 4 5 6 7 8 9 →List of numbers — Integers0 10 20 30 40 50 60 70 80 90 → | Cardinal | 1 one | Ordinal | 1st first | Numeral system | unary | Factorization | | Divisors | 1 | Greek numeral | α’ | Roman numeral | I | Roman numeral (Unicode) | Ⅰ‚ ⅰ | Persian | ١ - یک | Arabic | ١ | Ge’ez | ፩ | Bengali | ১ | Chinese numeral | 一，弌，壹 | Korean | 일‚ 하나 | Devanāgarī | १ | Telugu | ೧ | Tamil |
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of Engineering‚ Architecture‚ Fine Arts and Computing Sciences Gov. Pablo Borbon Campus II‚ Alangilan‚ Batangas City‚ Philippines 4200 In partial fulfillment of requirements in Software Engineering Software Requirements Specification NUMBER SYSTEMS CALCULATOR AND CONVERTER Presented by: Colico‚ Janine Erika R. Atendido‚ Mylene B. Atienza‚ Marianne C. BSIT-3201 To: Mr. Melvin Asa February‚ 2013 TABLE OF CONTENTS I. Introduction . . . . . . . . . . . . .
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8 Directed Numbers and the Number Plane This is the last time I fly El Cheapo Airlines! Chapter Contents 8:01 Graphing points on the number line NS4·2 8:02 Reading a street directory PAS4·2‚ PAS4·5 PAS4·2‚ PAS4·5 8:03 The number plane Mastery test: The number plane 8:04 Directed numbers NS4·2 NS4·2 8:05 Adventure in the jungle Investigation: Directed numbers 8:06 Addition and subtraction of directed NS4·2 numbers 8:07 Subtracting a negative number NS4·2 ID Card Learning
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understanding. Based on geometry alone‚ many special patterns evolve‚ such as the square numbers‚ triangular numbers‚ and much more. The Stellar Numbers are mostly used in astronomy and astrology. Stellar Numbers are figurate numbers based on the number of dots that can fit into a midpoint to form a star shape. The points of the star determine the number of points plotted around the midpoint. Triangular numbers is a figurate number system that can be represented in the form of a triangular grid of points where
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n Chinese tradition‚ certain numbers are believed by some to be auspicious (吉利) or inauspicious (不利) based on the Chinese word that the number name sounds similar to. The numbers 0‚ 6‚ 8‚ and 9 are believed to have auspicious meanings because their names sound similar to words that have positive meanings. Contents [hide] 1 Lucky numbers 1.1 Zero 1.2 Two 1.3 Three 1.4 Five 1.5 Six 1.6 Seven 1.6.1 Forty-nine 1.7 Eight 1.8 Nine 2 Unlucky numbers 2.1 Four 2.2 Five 2.3 Six 3 Combinations
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THE REAL NUMBER SYSTEM The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first‚ “number” meant something you could count‚ like how many sheep a farmer owns. These are called the natural numbers‚ or sometimes the counting numbers. Natural Numbers or “Counting Numbers” 1‚ 2‚ 3‚ 4‚ 5‚ . . . * The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever. At some point‚ the
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------------------------------------------------- Prime number A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime‚ as only 1 and 5 divide it‚ whereas 6 is composite‚ since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than
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NUMBER SYSTEMS TUTORIAL Courtesy of: thevbprogrammer.com Number Systems Number Systems Concepts The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar decimal (base 10) number system are used in the computer field. Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations. The binary number system is very efficient for computers‚ but not for humans. Representing
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