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Multiplicative inverse in factor ring?Hello, can someone tell me how to find the multiplicative inverse of an element in a factor ring? Let the element be f and the factor ring T[x]/(m). The basic idea is to solve a diophantine equation like f*u-m*v=1,right?and we need to find u |

You have the right idea – except that an element of $T[x]/(m)$ is of the form $f+(m)$ where $f$ is a polynomial of degree at most $\deg(m)-1$. When you have found a polynomial $u$ such that $fu=1+mv$ for some polynomial $v$, the multiplicative inverse of $f+(m)$ will be $u+(m)$. |

i see,thanks |

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