The euclidean algorithm

    • [DOC File]670 notes - Ohio State University

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      The Euclidean algorithm, applied to k and n, produces integers x and y for which kx + ny = 1. In (Z/nZ) the class of x is the inverse of the class of k. Example: See handout. What is the order of (Z/nZ) ? It is (n) = the number of pos. integers ≤ n which are relatively prime to n.

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    • [DOC File]Section 1: Rings and Fields

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      The Euclidean Algorithm makes repeated use of the division algorithm to find the greatest common divisor of two polynomials. If we are given two polynomials in where , then if , then , where is the monic polynomial obtained by factoring the leading coefficient of.

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    • [DOC File]Chapter 3 – Affine Cipher - TI89

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      The Euclidean Algorithm is a great example for the usage of the while-loop and is thus discussed in many introductory programming lectures. You will learn that a while-loop just as a do-while-loop are examples of indefinite loops which just means that number of runs is indefinite. (A for-loop, on the contrary, is a definite loop since the ...

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    • [DOCX File]Florida Atlantic University

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      The Continued Fractions Form of the Euclidean Algorithm in . F x This is essentially the form of the algorithm found in Berlekamp’s text on algebraic coding theory. You do not need to know continued fractions to follow it. The idea is to follow the standard, thousands-of-years-old process of successive divisions, while making “side ...

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    • [DOC File]Part one - Florida Atlantic University

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      The Euclidean Algorithm is used to find the greatest common divisor between two numbers. It is the solution to Proposition VII.2 in Euclid’s Elements: “To find the greatest common measure of two given numbers not relatively prime”. The algorithm is based on the following lemma with two observations:

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    • [DOC File]Section 4 - Radford University

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      The Euclidean Algorithm makes repeated use of the division algorithm to find the greatest common divisor of two numbers. If we are given two numbers a and b where , we comput /The last nonzero remainder, , is the greatest common divisor of a and b, that is, .

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    • [DOC File]Proof That Euclid’s Algorithm Works

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      Extended Euclidean Algorithm. One of the consequences of the Euclidean Algorithm is as follows: Given integers a and b, there is always an integral solution to the equation. ax + by = gcd(a,b). Furthermore, the Extended Euclidean Algorithm can be used …

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    • [DOC File]Gear Freq. Using Euclidean Algorithm

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      The Euclidean Algorithm is a time tested efficient method to find the GCD of two integers, and it can easily be programmed to compute the number of assembly phases for a gear as the following example shows. Since all our major gear trains require a hunting tooth combination per API 613 ,Special Purpose Gear Units For Refinery Service (third ...

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    • [DOC File]Chris Farley - Missouri State University

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      Note that this can be found using the Euclidean Algorithm. Compute the private key, d, which is the multiplicative inverse of i.e., find an integer d with In general, solve for d in the equation The existence of d follows from the fact that if given two integers, a and b, where the then b is invertible (mod a) and b has a multiplicative inverse in.

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    • [DOC File]Four Useful Algorithms: GCD, Subsets, Permutations and ...

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      Extended Euclidean Algorithm. Given that GCD(a,b) = c, it turns out that there is always a solution (in fact, an infinite number of solutions) to the equation. ax + by = c. Since c is a common factor in this equation, solving this equation is equivalent to solving the equation. a’x + …

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