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Extended Euclidean algorithm

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Extended Euclidean algorithm

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In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that
ax+by=\gcd. Wikipedia

The extended Euclidean algorithm is the essential tool for computing multiplicative inverses in modular structures, typically the modular integers and the ...

The gcd of two integers can be found by repeated application of the division algorithm, this is known as the Euclidean Algorithm. You repeatedly divide the ...

The Euclidean algorithm is arguably one of the oldest and most widely known algorithms. It is a method of computing the greatest common divisor (GCD) of two ...

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Oct 8, 2021 — The extended Euclidean algorithm updates results of gcd(a, b) using the results calculated by recursive call gcd(b%a, a). Let values of x and y ...

The recursive function above returns the GCD and the values of coefficients to x and y (which are passed by reference to the function). This implementation of ...

Aug 14, 2010 — The Euclidean algorithm is an efficient method to compute the greatest common divisor (gcd) of two integers. It was first published in Book VII ...

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The extended Euclidean algorithm is an extension to the Euclidean algorithm, which computes, besides the greatest common divisor of integers `a` and `b`, ...

We can formally describe the process we used above. This process is called the extended Euclidean algorithm . It is used for finding the greatest common divisor ...

The extended Euclidean algorithm is a modification of the classical GCD algorithm allowing to find a linear combination. From 2 natural inegers a and b, its ...