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

The Chinese remainder theorem We solve the congruences x a (mod m), x b (mod n). (See description of algorithm Enter a: Enter b: Last modified 23rd May 2003 Return to main page

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

A.A. Jagers A.A. Jagers

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

Chinese Remainder Theorem Find the two smallest counting numbers that will each have the remainders 2, 3, and 2 when divided by 3, 5, and 7 respectively. Correct Solutions: 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

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 Beginners 10 Easy Pieces Bouncing Ball A Card Trick? Cards #1 ... Multiple of 12? Intermediate 15 Puzzle #1 The 9321 Problem Aliquot Sums (Friendly If not Perfect) Alphametics ... Word Ladder Advanced 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

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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

Chinese remainder theorem Wikipedia The Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Table of contents showTocToggle("show","hide") 1 Simultaneous congruences of integers 2 Statement for principal ideal domains 3 Statement for general rings 4 External links Simultaneous congruences of integers 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.

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

Number Theory - Chinese Remainder Theorem BobHanlon Tue, 27 Mar 2001 08:50:03 +0200 (MET DST) Prev by Date: sounds in linux Next by Date: Counting Elements in a List Prev by thread: Number Theory - Chinese Remainder Theorem Next by thread: Number Theory - Chinese Remainder Theorem Index(es): Date Thread Search

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

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Chinese remainder theorem Chinese remainder theorem in the news The Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Simultaneous congruences of integers 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

See here for the ps.gz version Andrzej Solecki's cecinestpasunepeep Show proudly presents as m as n and x as x in the great Chinese Remainder Theorem index support file

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

Chinese Remainder Theorem Let and be Positive Integers which are Relatively Prime and let and be any two Integers . Then there is an Integer such that and Moreover, is uniquely determined modulo . An equivalent statement is that if , then every pair of Residue Classes modulo and corresponds to a simple Residue Class modulo The theorem can also be generalized as follows. Given a set of simultaneous Congruences for and for which the are pairwise Relatively Prime , the solution of the set of Congruences is where and the are determined from References A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 34-38, 1990. Uspensky, J. V. and Heaslet, M. A. Elementary Number Theory. New York: McGraw-Hill, pp. 189-191, 1939. Mathematica in Action. New York: W. H. Freeman, pp. 260-263, 1991. Eric W. Weisstein

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

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term Chinese remainder theorem The Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Inhaltsverzeichnis 1 Simultaneous congruences of integers 2 Statement for principal ideal domains 3 Statement for general rings 1 External Links Simultaneous congruences of integers 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

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

var google_language="en"; var adHB=true; wDoL("top","BLVQIEB"); wCls("BLVQIEB"); wDoL("btm","BLVQIEB"); showA("BLVQIEB"); The Chinese Remainder Problem 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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