1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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Ruler graduated in centimetres and millimetres‚ protractor‚ compasses‚ pen‚ HB pencil‚ eraser. Tracing paper may be used. Items included with question papers Nil Instructions to Candidates In the boxes above‚ write your centre number‚ candidate number‚ your surname‚ initials and signature. Check that you have the correct question paper. Answer ALL the questions. Write your answers in the spaces provided in this question paper. You must NOT write on the formulae page. Anything you write
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integers.Interestingly we can see some good theoretical discussion in Euclid’s “ELEMENTS” but no remark had been cited by Diophantus in his research works regarding this type of equations. 2.Whole Numbers: In number theory‚ we are usually concerned with the properties of the integers‚ or whole numbers: Z = {. . . ‚−3‚−2‚−1‚ 0‚ 1‚ 2‚ 3‚ . . .}. Let us begin with a very simple problem that should be familiar to anyone who has studied elementary algebra. • Suppose that dolls sell for 7 dollars each
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suggests the construction of a similar level inside a pair of glasses‚ which enables him to judge his balance by sight. "The Twins" - about autistic savants. Dr. Sacks tries to connect with twin brothers by joining their game of finding very large prime numbers. He cheats and uses a book; neither of them can read or even do multiplication. They instantly count 111 dropped matches simultaneously noticing that 111 is three 37s. [The book] is insightful‚ compassionate‚ moving and‚ on occasion‚ simply
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new millennium by equipping them with competitive life-long learning for understanding and ICT-fluency skills. When school children play Damath board game they also learn to explore‚ firm-up‚ deepen‚ and transfer to daily tasks the concepts of real numbers and its properties and operations. Moreover‚ it stimulates the children’s capability to think deeper through creative math storytelling‚ flowchart‚ concept map‚ tree diagram‚ picture riddle‚ haiku‚ cryptogram‚ secret code decoding‚ simulation‚ role
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However‚ it was not until a mathematician Thomas Nicely (of Lynchburg College in West Virginia) discovered the flaw during the summer/ fall of 1994 that it got in the news. He was computing the sum of the reciprocals of a large collection of prime numbers on his Pentium-based computer. Checking his computation‚ he found the result differed significantly from theoretical values. He did not get any real response to his initial queries to Intel. He then‚ after checking his facts‚ posted a general notice
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as important to me as readability and programming ease. I chose to implement RSA as the public key algorithm‚ and wanted to do this from scratch. I made the decision to write the cryptography algorithms from scratch anticipating that truly random numbers and big integers would provide important insight into some of the facets of cryptography‚ and I was not mistaken. I chose RSA (as opposed to other probably superior
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and quotes in this book‚ most of them are related to the main character‚ Christopher. It already starts with his introduction: "My name is Christopher John Francis Boone. I know all the countries of the world and their capital cities and every prime number up to 7‚507." (page 2). It’s a strange way of introducing yourself and therefore I found it funny. Christopher is actually really funny for the readers‚ but I understand if he is your son‚ that it’s not that amusing anymore. For example: He
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the number of awards won by one student. Answer: a) 6840 b)8000 2. Consider the word BASKETBALL: a. How many permutations are there? b. How many permutations begin with the letter K? c. How many permutations have the two L’s together? Answer: a) 453 600 b) 45 360 c) 90 720 3. How many 3-digit numbers can be formed using only the digits 1 to 7‚ if the number 2 must
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The Prime of Miss Jean Brodie Muriel Spark The following entry presents criticism on Spark’s novel The Prime of Miss Jean Brodie (1961). For further information on her life and works‚ see CLC‚ Volumes 2‚ 3‚ 5‚ 8 and 18. One of Spark’s best-known and most critically acclaimed works‚ The Prime of Miss Jean Brodie (1961) centers on morality‚ manipulation‚ and betrayal at a school for girls in Edinburgh‚ Scotland‚ during the 1930s. Praised for its structural complexity‚ the novel juxtaposes past‚ present
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