Kriptoloji Ders 3

\boxed{
a.c=b.c(mod~m) \land gcd(c,m) = 1 \Rightarrow c^{-1}(mod~m)
}

\boxed{
a.c.c^{-1} = b.c.c{-1}(mod~m)\\a=b(mod~m)
}

\boxed{
\begin{align*}
40&=25(mod~3)\\
8.5&=5.5\\
8&=5(mod~3)
\end{align*}
}

\boxed{
\begin{align*}
14&=8(mod~6)\\
7.2&=4.2(mod~6)\\
7&=4(mod~6)
\end{align*}
}

a.c=b.c~(mod~m) \land gcd(c,m)=i \\
\Rightarrow a=b(mod~k) \land (k=m/i)

a.x=b~~(mod~m) \land gcd(a,m)=1 \\
\Rightarrow x=a^{-1}.b~~(mod~m)

3.x=4~~(mod~7) \Rightarrow x=?

\alpha\equiv 1(mod~p) \Rightarrow \alpha^n \equiv 1(mod~p)