For example: $$7x \\equiv 1 \\pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a

For example, consider the problem of finding the inverse of 5 modulo 164. It's easy to see that 164 when divided by 5 leaves a remainder of 4, which means 164 is congruent to -1 mod 5.

May 10, 2015 · Here's an illustration of finding the multiplicative inverse of 37 mod 100 using the extended Euclidean algorithm. (I used bigger numbers for this example so that the relationships are …

For small moduli it is easy to find the modular inverse of a number by brute-force. For larger numbers, the extended euclidean algorithm is an effective way to calculate the modular inverse of a number.

Jan 4, 2015 · Fastest way to find modular multiplicative inverse Ask Question Asked 10 years, 11 months ago Modified 5 years, 1 month ago

Apr 9, 2014 · Extended Euclidean Algorithm for Modular Inverse Ask Question Asked 11 years, 8 months ago Modified 6 years, 9 months ago

Apr 24, 2017 · 2 Find an inverse for $43$ modulo $600$ that lies between $1$ and $600$, i.e., find an integer $1 \leq t \leq 600$ such that $43 \cdot t \equiv 1 (\text { mod } 600)$. The solution below …

Nov 17, 2022 · There's an algorithm similar to Buchberger's algorithm to calculate a nice generating set of an ideal of $\mathbb {Z} [X]$. So in your example, applying that to the ideal $\langle 4, 2X+1, X^3 …

Aug 15, 2014 · Recently I have read extended euclid's algorithm which is used to find out the modular inverse of a number N whith respect to MOD such that $\\gcd(N,MOD)=1.$ But I have a doubt that …

Mar 11, 2018 · I find the modular multiplicative inverse (of the matrix determinant, which is $1×4-3×5=-11$) with the extended Euclid algorithm (it is $-7 \equiv 19 \pmod {26}$).