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Chinese Remainder Theorem:     more detail

Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography by C. Ding, D. Pei, et all 1999-06 Secret Sharing Using the Chinese Remainder Theorem: Secret Sharing, Chinese Remainder Theorem, Threshold Cryptosystem, Cardinality, Access Structure, Shamir's ... Polynomial Interpolation, George Blakley Remainder: Natural Number, Real Number Modulo Operation, Chinese Remainder Theorem, Division Algorithm, Euclidean Algorithm A hierarchical single-key-lock access control using the Chinese remainder theorem (OSU-CS-TR) by Kim Sin Lee, 1994 Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications) by Richard A. Mollin, 1998-01-31 Fundamental Number Theory with Applications, Second Edition (Discrete Mathematics and Its Applications) by Richard A. Mollin, 2008-02-21

lists with details

61. The Chinese Remainder Theorem
    The chinese remainder theorem. We solve the congruences x a (modm), x b (mod n). (See description of algorithm.) Enter a Enter  
    http://www.numbertheory.org/php/chinese2.html

62. Chinese Remainder Theorem
    AA Jagers.  
    http://wwwhome.cs.utwente.nl/~jagersaa/152063/CRS/Main.html

63. Chinese Remainder Theorem
    chinese remainder theorem. Find the two smallest counting numbers that will eachhave the remainders 2, 3, and 2 when divided by 3, 5, and 7 respectively.  
    http://pegasus.cc.ucf.edu/~ucfcasio/pow/chinese.htm
    
    Extractions: Yona Levine. Lehava, Kedumim, Israel Xingji Zheng. Abby Senior SS, Abbotsford, BC, Canada Michael Moyer. The Way Home School, Carlisle, PA Bella Voldman. Brookline HS, Brookline, MA Stephan Wild. BSZ 3, Leipzig, Germany Shu Duan. Ecole Marie-Esther, Shippagan, New Brunswick, Canada Lisa Goliber. Spalding Catholic, Granville, IA Edgar Pantoja. Carteret HS, Carteret, NJ Wojciech Lewkowicz. Lemont HS, Lemont, IL Amanda Vicary. Farmington HS, Farmington, IL Paul Pollack. Gulf HS, New Port Richey, FL Gregory Winston. O'Neill CVI, Oshawa, Ontario, Canada David Sorani. Shaare HS, Brooklyn, NY Ido Yariv. Gan-Nachum School, Rishon LeZion, Israel Kenny Ho. Gordon Graydon SS, Mississauga, Ontario, Canada Katie Dawson. Newnan HS, Newnan, GA Amit Sahasrabudhe. TL Kennedy, Mississauga, Ontario, Canada Sameer Akhtar. TL Kennedy, Mississauga, Ontario, Canada Fang Yi Liu. South Hills HS, Covina, CA

64. Time Efficient Chinese Remainder Theorem Algorithm For Full-field Fringe Phase A
    6, March 22, 2004, Page 1136 1143. Time efficient chinese remainder theorem algorithmfor full-field fringe phase analysis in multi-wavelength interferometry.  
    http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1136

65. Chinese Remainder Theorem,characteristic
    From Paulette Date Nov 6, 2003 Subject chinese remainder theorem,characteristicPlease somebody help me. 1)Show that if a is  
    http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2003&task=show_msg&msg=0

66. Re: Chinese Remainder Theorem,characteristic
    From mars Date Nov 7, 2003 Subject Re chinese remainder theorem,characteristic. Usethis and the chinese remainder theorem to show that if.  
    http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2003&task=show_msg&msg=0

67. Chinese Remainders
    The chinese remainder theorem is not particularly easy to understand it justsays that under certain conditions (ie the divisors have no common factors  
    http://www.delphiforfun.org/Programs/chinese_remainders.htm
    
    Extractions: Home Introduction About Delphi Feedback ... Site Search (bottom of page) Available Now (Click a duck below to expand program list if it is collapsed - MS Internet Explorer only) There is also a computer generated program index page here 10 Easy Pieces Bouncing Ball A Card Trick? Cards #1 ... Multiple of 12? 15 Puzzle #1 The 9321 Problem Aliquot Sums (Friendly If not Perfect) Alphametics ... Word Ladder 15 Puzzle #2 Airport Simulation Akerue Astronomy Demo ... WordStuff 2 Contact Feedback Send an e-mail with your comments about this program (or anything else). Search WWW Search delphiforfun.org Problem Description What is the smallest number that can be divided by 6, leaving a remainder of 5; by 5 leaving 4; and by 4 leaving 3? Source: The Mensa (c) Puzzle Calendar for Oct 18. 2001; Here's an introduction to Chinese Remainder problems. They're called "Chinese Remainder" because the problem and the theorem which defines when they can be solved were both known to the early Chinese scholars. The earliest known example of this type of problem was published in the 3rd, 4th or 5th century AD by Chinese scholar, Sun Zi, in a book titled "

68. Bookmarks2 For Patrick Reany
    generalizations Rings. chinese remainder theorem. Reany s Heuristicsof chinese remainder theorem Math 5410 chinese remainder theorem  
    http://www.ajnpx.com/html/Bookmarks2.html

69. Chinese Remainder Theorem
    The chinese remainder theorem is any of a number of related results in abstractalgebra and number theory. External Links. chinese remainder theorem.  
    http://www.xasa.com/wiki/en/wikipedia/c/ch/chinese_remainder_theorem.html
    
    Extractions: 4 External links The original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences Furthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set e i s n n i , then we have The number x i k a i e i then solves the given system of simultaneous congruences.

70. MathGroup Archive (2001/03) - Number Theory - Chinese Remainder Theorem
    Number Theory chinese remainder theorem. BobHanlon Tue, 27 Mar 2001 085003+0200 (MET DST). Next by thread Number Theory - chinese remainder theorem;  
    http://hilbert.math.hr/arhive/mathgroup/2001/03/0488.html

71. Chinese Remainder Theorem
    Article on chinese remainder theorem from WorldHistory.com, licensedfrom Wikipedia, the free encyclopedia. chinese remainder theorem.  
    http://www.worldhistory.com/wiki/C/Chinese-remainder-theorem.htm
    
    Extractions: World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Chinese remainder theorem in the news The Chinese remainder theorem is any of a number of related results in abstract algebra and number theory The original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao published in , is a statement about simultaneous congruences (see modular arithmetic). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences x a i mod n i ) for i k Furthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set e i s n n i , then we have e i mod n i ) and e i mod n j ) for j i The number x i k a i e i then solves the given system of simultaneous congruences.

72. Chinese Remainder Theorem Can Be Seen
    See here for the ps.gz version. Andrzej Solecki s cecinestpasunepeep Show. proudlypresents 5 as m, 4 as n and x as x in the great. chinese remainder theorem. !  
    http://jurere.mtm.ufsc.br/~andsol/english/mat/china.html

73. Chinese Remainder Theorem
    chinese remainder theorem. Wagon, S. ``The chinese remainder theorem. §8.4in Mathematica in Action. New York W. H. Freeman, pp. 260263, 1991.  
    http://icl.pku.edu.cn/yujs/MathWorld/math/c/c271.htm

74. Chinese Remainder Theorem Definition Meaning Information Explanation
    dir_id AND dv.dir_version=0 AND dv.dir_status_id = 0 AND dv.site_id = 1 AND odr.odr_version= 0 AND odr.odr_filename= chineseremainder-theorem.html AND ov  
    http://www.free-definition.com/Chinese-remainder-theorem.html
    
    Extractions: 1 External Links The original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences Furthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set

75. The Chinese Remainder Problem
    It has given rise to such terms as chinese remaindering and chineseremainder theorem. There even is a book entirely devoted to it.  
    http://www25.brinkster.com/ranmath/diophan/chinese.htm
    
    Extractions: var google_language="en"; var adHB=true; wDoL("top","BLVQIEB"); wCls("BLVQIEB"); wDoL("btm","BLVQIEB"); showA("BLVQIEB"); There is a number which divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What is the number? Sun Tsu Suan Ching (4th century AD) The above is a classic problem that has had considerable impact. It has given rise to such terms as "Chinese remaindering" and "Chinese remainder theorem." There even is a book entirely devoted to it. The problem usually is formulated in modular number notation but here we shall use the equivalent arbitrary integer constant notation. N = 3t + 2 N = 5u + 3 N = 7v + 2 This is a system of three linear Diophantine equations in four unknowns. In solving the system algebraically the usual procedure is to substitute the first equation into the second, resulting in a single equation in two unknowns. This is solved for t or u in terms of a new arbitrary integer variable. This solution for N then is substituted into the third equation which is then solved for v. Once v is known, then N can be calculated from the last equation. Let's do it!

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