diff --git a/content/english/hpc/number-theory/euclid-extended.md b/content/english/hpc/number-theory/euclid-extended.md index a37c1b29..ff2cd8f8 100644 --- a/content/english/hpc/number-theory/euclid-extended.md +++ b/content/english/hpc/number-theory/euclid-extended.md @@ -11,7 +11,7 @@ $$ where $\phi(m)$ is [Euler's totient function](https://en.wikipedia.org/wiki/Euler%27s_totient_function) defined as the number of positive integers $x < m$ that are coprime with $m$. In the special case when $m$ is a prime, then all the $m - 1$ residues are coprime and $\phi(m) = m - 1$, yielding the Fermat's theorem. -This lets us calculate the inverse of $a$ as $a^{\phi(m) - 1}$ if we know $\phi(m)$, but in turn, calculating it is not so fast: you usually need to obtain the [factorization](/hpc/algorithms/factorization/) of $m$ to do it. There is a more general method that works by modifying the [the Euclidean algorthm](/hpc/algorithms/gcd/). +This lets us calculate the inverse of $a$ as $a^{\phi(m) - 1}$ if we know $\phi(m)$, but in turn, calculating it is not so fast: you usually need to obtain the [factorization](/hpc/algorithms/factorization/) of $m$ to do it. There is a more general method that works by modifying the [Euclidean algorthm](/hpc/algorithms/gcd/). ### Algorithm