by Manindra Agrawal‚ Neeraj Kayal‚ and Nitin Saxena‚ computer scientists at the Indian Institute of Technology Kanpur‚ on August 6‚ 2002‚ in a paper titled "PRIMES is in P".[1] The authors received many accolades‚ including the 2006 Gödel Prize and the 2006 Fulkerson Prize‚ for this work. The algorithm determines whether a number is prime or composite within polynomial time. Contents 1 Importance 2 Concepts 3 History and running time 4 Algorithm 5 References 6
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Java Sample Program 1. Write a program in Java that allows the user to enter a number and then display its Pascal’s Triangle -The triangle is bordered by ones on the right and left sides‚ and each interior entry is the sum of the two entries above. Sample Input/Output: Please enter a value for Triangle: 6 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Solution: import java.io.*; import java.util.*; public class Triangle
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transactions and transmissions‚ such as fund transfers. The security of the RSA algorithm has so far been validated‚ since no known attempts to break it have yet been successful‚ mostly due to the difficulty of factoring large numbers n = pq‚ where p and q are large prime numbers. 1 Public-key cryptosystems. Each user has their own encryption and decryption procedures‚ E and D‚ with the
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"Museum"‚ and that he wrote the most enduring mathematical work of all time‚ the Stoicheia or Elements‚ a thirteen volume work. The Elements or Stoicheia is divided into thirteen books. The books go over plane geometry‚ arithmetic and number theory‚ irrational numbers‚ and solid geometry. Euclid organized the known geometrical ideas‚ starting with simple definitions‚ axioms; formed statements called theorems‚ and set forth methods for logical proofs. He began with accepted mathematical truths‚ axioms
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epimorphisms . . . . . . . . . . . . . . . . . . 1.2.4 Endomorphisms and automorphisms . . . . . . . . . . . . . . . . . 1.3 A little number theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Mathematical induction on the natural numbers N . . . . . . . . . 1.3.2 Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Prime numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 The Euclidean algorithm . . . . . . . . . . . . . . . . . .
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Essay: The Curious Incident of the Dog in the Night-time by Mark Haddon To what extent is Christopher’s condition responsible for the conflict the arise in the curious incident of the dog in the night-time? 1. Underline the keyword To what extent: How far or how much Christopher’s condition: Asperger autism Responsible: Blamed for cause Conflict: problems or difficulties - reverse: good things 2. Rewrite the Question: How far is Christopher’s Asperger syndrome to blame for problems that occur in
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Problem 7: Bigger than 100? Write a C program that reads a number from the keyboard via the scanf function‚ and then prints the message The number is bigger than 100 if it is. If the number is 100 or less than 100 then you should print out the message The number is not bigger than 100. Problem 8: One Line of Asterisks Create a file called testdata8 that has a single integer value stored into it. The integer will be a number between 1 and 30 inclusive. Create a C program that uses the fscanf
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THE IMPORTANCE OF MATHEMATICS W. T. Gowers It is with some disbelief that I stand here and prepare to address this gathering on the subject of the importance of mathematics. For a start‚ it is an extraordinary honour to be invited to give the keynote address at a millennium meeting in Paris. Secondly‚ giving a lecture on the significance of mathematics demands wisdom‚ judgment and maturity‚ and there are many mathematicians far better endowed than I am with these qualities‚ including several
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Christopher and others. Choose 10 questions. Answer each of those questions in 1-2 paragraphs per answer. Write in full and proper sentences‚ not dot points (even though they are used here to clarify what you are to do) Make sure you clearly number and/or include the question that you are answering. 1. Read the first paragraph of the novel (p.1). • What do you learn about Christopher by reading this passage? • What do you learn about what is important to him? • How does he
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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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