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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DEAD MAN’S PATH by CHINUA ACHEBE The title of this story "Dead Man’s Path" foreshadows the series of events about to take place in the story. "Dead Man’s Path" does not only refer to the ancestral pathway but also refers to Obi’s choice of action. His "path" by not compromising has made him a "Dead Man". Dead in this context is not death‚ but is referring to his failure. His dream died. The title also foreshadows dark events that would occur in the story. Meaning this story has quite a sad ending
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MANKIND KILLING OUR PLANET. Our planet contains a variety of landscapes‚ forests and different climates. Over the years it has gone through many changes in its climate and the species that live on it. Now it seems that our planet is being detrimentally transformed‚ not by natural events‚ but by the actions of one species-mankind. Are we as humans changing planet earth? The facts certainly show that there has been a change in climate and that it is Human induced. It has become noticeably hotter
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Ecosystem Services and Their Importance to Mankind University of Illinois at Chicago Introduction: Although technological advances over recent centuries have surpassed unfathomable expectations‚ those services most essential to the survival of mankind are provided for‚ freely‚ by natural occurring events taking place regularly in our ecosystems. The purification of air and water‚ protection against droughts and floods‚ reduction of greenhouse gases‚ decomposition of organic matter‚ preservation
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❖ S 9: “Officer” includes directors‚ secretaries‚ receivers‚ administrators‚ liquidators‚ administrating trustees. ❖ S 9: “Director” includes shadow & de facto directors. enforcement of directors’ duties enforcement of statutory duties Civil penalties Who may apply for a Declaration or Order? ❖ S 1317J(1): ASIC may apply for a declaration of contravention‚ a pecuniary penalty order or a compensation order. ❖ S 1317J(2): The company may apply for a compensation order. ❖
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better than anyone else; someone who is closer than you might expect? Sir Thomas Browne once said “Every man is his greatest enemy‚ and as it were‚ his own executioner”. Keeping that thought in mind‚ the question that remains unanswered is who is man’s greatest enemy? Wayne LaPierre from the NRA once said “Guns don’t kill people”. While there are many arguments with regards to this topic‚ one thing is quite certain and that an inanimate object is not able to cause harm by itself. However‚ when
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WHAT IS DUTY? It is necessary in the study of Karma-Yoga to know what duty is. If I have to do something I must first know that it is my duty‚ and then I can do it. The idea of duty again is different in different nations. The Mohammedan says what is written in his book‚ the Koran‚ is his duty; the Hindu says what is in the Vedas is his duty; and the Christian says what is in the Bible is his duty. We find that there are varied ideas of duty‚ differing according to different states in life‚ different
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List of Prime Ministers of India From Wikipedia‚ the free encyclopedia Jump to: navigation‚ search The complete list of Prime Ministers of India includes the persons sworn into the office as Prime Minister of India following the proclamation of the independence of India in 1947. Key: No.: Incumbent No. CM: Council of Ministers Congress: Indian National Congress‚ Indian National Congress (Indira)‚ United Progressive Alliance Bharatiya Janata Party: Bharatiya Janata Party‚ National
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The article Server or Fail‚ by Dave Eggers of The New York Times presents a very interesting take on college students and their free time. Eggers believes that colleges should institute a service requirement for students to graduate. Due to his college experience he considers college students to have too much spare time‚ which is wasted on silly electives or just wasted. With this surplus of time students should contribute to the community around themselves to develop intellectual tools that will
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Most important scientific discovery by mankind ever Geoffrey Macharia Maseno University Most important scientific discovery by mankind It is a fact that science continues to play a significant role in the existence of mankind and the extent to which he relates to the universe. Man has continued to make great scientific discoveries that have made it possible for him to exploit most of the natural resources to his advantage. Increase in world population has led to a major
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