WebFeb 6, 2024 · An efficient solution is based on extended Euclid algorithm. Extended Euclidean algorithm finds integer coefficients x and y such that: ax + by = gcd (a, b) Let us put b = prime, we get ax + prime * y = gcd (a, prime) We know gcd (a, prime) = 1 because one of the numbers is prime. WebJul 12, 2024 · $\begingroup$ The extended Euclidean (and related) algorithms do indeed use remainder calculations, which can be calculated by long division as above. However, generally such algorithms require many such remainder calculation steps, not only a single step as above. As for that particular inverse calculation, it is simpler to divide $\,120\div …
The Euclidean Algorithm (article) Khan Academy
WebMar 15, 2024 · 1 Answer. Well, you can try starting from Extended Euclid Algorithm, e.g. (let it be implemented as extension methods) public static (BigInteger LeftFactor, … WebMar 15, 2024 · public static BigInteger ModInversion (this BigInteger value, BigInteger modulo) { var egcd = Egcd (value, modulo); if (egcd.Gcd != 1) throw new ArgumentException ("Invalid modulo", nameof (modulo)); BigInteger result = egcd.LeftFactor; if (result (left * ModInversion (right, modulo)) % modulo; … is dancing relaxing
Extended Euclidean Algorithm and Inverse Modulo …
WebExtended Euclidean algorithm; Modular multiplicative inverse; 1. Modular arithmetic. When one number is divided by another, the modulo operation finds the remainder. It is denoted by the $$\%$$ symbol. Example. Assume that you have two numbers 5 and 2. $$5 \%2 $$ is 1 because when 5 is divided by 2, the remainder is 1. Properties WebMay 27, 2024 · Modular multiplicative inverse Extended Euclidean algorithms Can we always do modular division? The answer is “NO”. First of all, like ordinary arithmetic, division by 0 is not defined. For example, 4/0 is not allowed. In modular arithmetic, not only 4/0 is not allowed, but 4/12 under modulo 6 is also not allowed. WebThe extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation. By reversing the steps in the Euclidean algorithm, it is possible to find … is dancing sinful