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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TUTORIAL: NUMBER SYSTEM 1. Determine whether each statement is true or false a) Every counting number is an integer b) Zero is a counting number c) Negative six is greater than negative three d) Some of the integers is natural numbers 2. List the number describe and graph them on the number line a) The counting number smaller than 6 b) The integer between -3 and 3 3. Given S = {-3‚ 0‚[pic]‚ [pic]‚ e‚ ‚ 4‚ 8…}‚ identify the set of (a) natural numbers (b) whole numbers (c) integers
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Name Chapter 2‚ Lesson 1 Practice Date Hands On: Compare and Order Whole Numbers CA Standard NS 1.2 Use > or < to compare the numbers. Make a number line on a separate sheet of paper to help. 1. 4‚351 4. 119‚832 7. 9‚889 4‚315 2. 8‚998 5. 745‚271 8. 911‚238 60‚060 6‚600 30‚298 75‚271 30‚302 3. 69‚780 6. 598‚401 9. 14‚501 96‚870 589‚410 13‚799 Test Practice Circle the letter of the correct answer. 10.
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internationally by scholars and researchers. This style has two elements: In-text citations In the body of your paper‚ give the surname of the author and the date of publication. Also give the page number if you quote a passage directly or if you paraphrase (put the idea into your own words). List of References At the end of your paper‚ give full publication or internet information so that a reader can easily locate your sources In-text Citations You must cite every source you refer to
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|01/06/11 |V |- |- |5 |1 |4 |1 |4 |15 | | |S |- |- |2 |0 |1 |0 |2 |5 | |06/06/11 |V |3 |2 |1 |5 |1 |1 |1 |14 | | |S |2 |1 |0 |2 |0 |0 |0 |5 | |13/06/11 |V |5 |2 |4 |3 |1 |2 |0 |17 | | |S |2 |0 |2 |1 |0 |1 |0 |6 | |20/06/30 |V |3 |3 |7 |6 |4 |4 |0 |27 | | |S |1 |2 |3 |2 |0 |0 |0 |8 | |27/06/11 |V |1 |4 |6 |4 |- |- |- |15 | | |S |0 |2 |3 |0 |- |- |- |5 | | | | | | | |Total visitors |88 | | | | | | | |Total Sales |29 | | Mean: The average (mean) number of daily visitor traffic is 3 (total amount of
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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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he number theory or number systems happens to be the back bone for CAT preparation. Number systems not only form the basis of most calculations and other systems in mathematics‚ but also it forms a major percentage of the CAT quantitative section. The reason for that is the ability of examiner to formulate tough conceptual questions and puzzles from this section. In number systems there are hundreds of concepts and variations‚ along with various logics attached to them‚ which makes this seemingly
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polyatomic ions). 1. Determine the Number of valence electrons in the Lewis Structure: One of the easiest ways to start drawing a Lewis Structure is to make a list of each atom in the structure and next to each atom record how many valence electrons it has and how many it needs to fill its valence shell. In covalent bonding the valence electrons in the molecule come from the valence electrons in the atoms that formed the bond. a. The number of valence electrons in any main group atom
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Abstract A complex number is a number that can be written in the form of a+bi where a and b are real numbers and i is the value of the square root of negative one. In the form a + bi‚ a is considered the real part and the bi is considered the imaginary part. The goal of this project is show how the use of complex numbers originates in the history of mathematics. Introduction Complex numbers are very important component of mathematics. They enable us to solve any polynomial equation of degree
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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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