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Given the following linear congruence: $ax \equiv b \mod n $

In the case when GCD($a,n$)=1, is it true that the value of x can be found using Extended Euclidean Algorithm, i.e. $x$ = E-GCD($a,n$) ?

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Yes, the algorithm will return $(u,v)\in\mathbb{Z}^2$ such that $au+nv=1$. Therefore, $x=ub$ is a solution of the given equation.

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