------------------------------------------------- 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
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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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The Prime Minister of India‚ as addressed to in the Constitution of India‚ is the chief of government‚ chief advisor to the President of India‚ head of the Council of Ministers and the leader of the majority party in parliament. The prime minister leads the executive branch of the Government of India. The prime minister is the senior member of cabinet in the executive branch of government in a parliamentary system. The prime minister selects and can dismiss other members of the cabinet; allocates
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The Prime Minister is the most important and powerful executive of the state. He can be called the ruler-of the state. He is the head of the Council of Ministers and all the powers of the President are actually exercised by the ministers. He can rule the country in a way which he thinks the best. He is the architect of the fate of state. Appointment The Prime Minister is appointed by the President but while doing so the President is not having a free hand. Only that person can be appointed to the
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Gems from the world of data structures and algorithms Bit-Sum Prime Difficulty level: moderate Every student‚ who has learned programming‚ must have written a program to determine whether a given positive integer is a prime number. Basically in order to determine whether a positive integer n is prime‚ we search for any number in the range [2‚ n − 1] which can divide n. Some of you would have designed a slighly better implementation where you search √ for any divisor of
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The Reality of Reality Television Jacqueline Knudsen ENG122: English Composition II Jenna Fussell February 2‚ 2013 The Reality of Reality Television Have you ever set there watching your favorite reality television show and wondered what effects it could have on you‚ your family or your friends? Truth is most people do not think about the effects television shows can have before watching them or allowing their children to watch them. This
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The Reality of Virtual RealityMelissa JessINF1034/15/2013 Instructor Mark Cohen THE REALITY OF VIRTUAL REALITYVirtual reality used to be a thing of the future‚ well the future is now. Virtual reality is an environment created through the use of computers. It can be either a real world environment or a fantasy world. Most of the virtual reality is depicted through the visual sense‚ however there are some that use the other senses to help create more of a feeling that you are in the virtual world
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Analyzing the speech ‘What Educated Women Can Do’ by Indira Gandhi‚ published in the Selected Speeches and Writings of Indira Gandhi from September 1972 to March 1977 (WordPress.com 2011) stresses on the importance of women’s education and their neglect not only in India but around the whole world. In this speech‚ Gandhi provides many strong stances on women’s education. Gandhi discusses its culture and superstitions and how women in India have been oppressed of proper/formal education. She also
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When people aren’t living life the way they expect‚ they tend to find a way of coping with their issues. Every reality poses problems‚ some people find ways of hiding from their problems or in other words escaping from reality. Each of the unique main characters‚ Amanda‚ Laura‚ and Tom‚ in Tennessee Williams play‚ The Glass Menagerie‚ have a difficulty accepting reality and have several ways of escaping from the problems. Laura is painfully shy which affects how she interacts with others in the
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Across history‚ several authors have expressed the idea of reality based on what the mind says is real or not; from George Berkley to Rene Descartes‚ the way perceptions affect reality has been discussed. Christopher Nolan through the film Inception uses Descartes and Berkeley’s theories as a method to catch viewers’ attention by belying dogmas than have been imposed on humanity. For Rene Descartes‚ the thinking‚ and thus the existence‚ is undeniable‚ absolutely true and from which one new certainties
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