Anmol Mehrotra Pythagorean triples Math Bonus A Pythagorean triple consists of three positive integers a ‚ b ‚ and c ‚ such 2 2 2 that a + b = c . Such a triple is commonly written ( a ‚ b ‚ c )‚ and a wellknown example is (3‚ 4‚ 5). If ( a ‚ b ‚ c ) is a Pythagorean triple‚ then so is ( ka ‚ kb ‚ kc ) for any positive integer k . A primitive Pythagorean triple is one in which a ‚ b
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where p is prime and g is primitive root mod p. Here is an example of the protocol‚ with non-secret values in blue‚ and secret values in boldface red: Alice | | Bob | Secret | Public | Calculates | Sends | Calculates | Public | Secret | a | p‚ g | | p‚g | | | b | a | p‚ g‚ A | ga mod p = A | A | | p‚ g | b | a | p‚ g‚ A | | B | gb mod p = B | p‚ g‚ A‚ B | b | a‚ s | p‚ g‚ A‚ B | Ba mod p = s | | Ab mod p = s | p‚ g‚ A‚ B | b‚ s | | | | 1. Alice and Bob agree to use a prime number p=23 and
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Prime Minister Hawke perceived there to be a substantial imbalance in the distribution of power and influence in the executive‚ towards permanent rather than elected political officials (Halligan‚ 2013‚ 115)‚ and viewed advisers as the key tool to overcome
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called (i) odd numbers (ii) prime numbers (iii) composite numbers (e) The number 1 is (i) prime number (ii) composite number (iii) neither prime nor composite (f) 7 in decimal form is written as 100 (i) 0.7 (ii) 0.07 (iii) 0.007 Q2. Fill in the blanks: 6M (a) To make profit Selling price is __________________ (greater/ smaller) than the Cost price. (b) A part of a whole is called _______________ (composite/ fraction). (c) A prime number has exactly _____________
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REAL NUMBERS Q.1 Determine the prime factorization of the number 556920. (1 Mark) (Ans) 23 x 32 x 5 x 7 x 13 x 17 Explanation : Using the Prime factorization‚ we have 556920 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13 x 17 = 23 x 32 x 5 x 7 x 13 x 17 Q.2 Use Euclid’s division algorithm to find the HCF of 210 and 55. (1 Mark) (Ans) 5 Explanation: 5 ‚ Given integers are 210 and 55 such that 210 > 55. Applying Euclid’s division leema to 210 and 55‚ we get 210 = 55 x 3 + 45 ………
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schools‚ colleges and government organization to remember the day that we became a free nation. There is an official ceremony held at the Red Fort in the National Capital. The Prime Minister of India hoists the Tricolor at the Red Fort to commemorate Independence Day and to honor our freedom fighters. The Prime Minister’s speech at the Red Fort in Delhi is a
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European Parliament It is the only directly elected body of the European Union They have 754 members (MEPs) They are elected once every 5 years through turnout for voting is low The EP drafts EU legislations which affects UK‚ which we must adhere to‚ but we can still make up our own laws They also control the EU budgets It has 2 places of work; Brussels in Belgium‚ Luxemburg city‚ Strasbourg in France Advantages of being in the EU I believe an advantage of being in the European Union is
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What is debate?? Debate is a method of interactive and representational argument. The goal of a debate is basically to solve a certain issue or problem Structure Speaker Roles Prime Minister (First Affirmative) • Define the motion • Provide clarity and precision on exactly what the subject of the debate is Set-up your case – elaborate what your side wants (stance) and how you want to go about it Provide an outline of the team’s case Present and develop your arguments Summarize Speaker
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Advantages of Monarchy Patriotism: Monarchs‚ by their very nature‚ are more patriotic than either Prime Ministers or Presidents. They hold great affection for their respective countries: a Prime Minister or President may be at the same post in other countries but Monarchs never have this conflict of interest. So‚ fundamentally‚ it is in the interest of any monarch to work towards greater patriotism. Every monarch makes a considerable contribution in the building of his or her nation. One who contributes
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infinitive “gubernare‚” which means “to govern” or “to manage”. In the parliamentary systems‚ the word government is often used; however‚ in the presidential systems what you hear is the executive branch. The parliamentary system of government has a prime minister and a cabinet; in other cases government refers to executive‚ legislative‚ bureaucratic of judicial. In this paper‚ a comparative analysis of two systems of governments will be undertaken such as the British system of government and the French
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