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Modular arithmetic was studied first by Carl Friedrich Gauss and was written about in his book Disquisitiones Arithmeticae in 1801. ... History Forum; Come and discuss about History, Civilizations, Historical Events and Figure...
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www.spiritus-temporis.com/modular-arithmetic/history.ht...
www.spiritus-temporis.com/modular-arithmetic/history.html
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Modular (often also Modulo) Arithmetic is an unusually versatile tool discovered by K.F.Gauss (1777-1855) in 1801. Two numbers a and b are said to be equal or congruent modulo N iff N|(a-b), i.e. iff their difference is exactly divisible by N. Usually (and on this page) a,b, ... Oystein Ore, Number Theory and Its History,
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www.cut-the-knot.org/blue/Modulo.shtml
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Modular arithmetic. The generalized theorem of Fermat and its converse versions, including Carmichael numbers and stochastic primality testing. ... Modular arithmetic: The algebra of congruences, formally introduced by Gauss.
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home.att.net/~numericana/answer/modular.htm
home.att.net/~numericana/answer/modular.htm
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Modular arithmetic is a modified system of arithmetic for integers, sometimes referred to as "clock arithmetic", where numbers "wrap around" after they reach a certain value (the modulus). ... Modular arithmetic is applied in number theory, abstract algebra, cryptography, and visual and musical art.
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fact-archive.com/encyclopedia/Modular_arithmetic
fact-archive.com/encyclopedia/Modular_arithmetic
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Conway, J. H. and Guy, R. K. "Arithmetic Modulo p ." In The Book of Numbers. New York: Springer-Verlag, pp. 130-132, 1996. Courant, R. and Robbins, ...
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mathworld.wolfram.com/Congruence.html
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Under modular arithmetic (with mod N), the only numbers are 0, 1, 2, …, N − 1, and they are known as residues modulo N. Residues are added by taking the usual arithmetic sum, then subtracting the modulus from the sum as many times as is necessary to reduce the sum to a number M between 0 and N − ... TOPIC HISTORY...
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www.britannica.com/EBchecked/topic/920687/modular-arith...
www.britannica.com/EBchecked/topic/920687/modular-arithmetic
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In arithmetic modulo non-primes, the cancellation law no longer holds. For example, in arithmetic modulo 12, is the product of two non-zero numbers which gives you zero. In such number systems, you cannot divide by all non-zero numbers.
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www.math.toronto.edu/mathnet/simmer/topic.may97_3.html
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Dictionary: modular arithmetic ... A familiar use of modular arithmetic is its use in the 12-hour clock, in which the day is divided into two 12 hour periods. ... History, Politics, Society...
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www.answers.com/topic/modular-arithmetic
www.answers.com/topic/modular-arithmetic
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To expand search, see Arithmetic. ... The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines.
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mtcs.truman.edu/~thammond/history/ResidueClasses.html
mtcs.truman.edu/~thammond/history/ResidueClasses.html
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