Reduced Set of Residues
\[n\]
can be found once we have any reduced residue. For example 5 is a reduced residue modulo 14, meaning that \[gcd(5,14)=1\]
. A reduced set of residues is \[\{ 1, \; 3, \; 5, \; 9, \; 11, \; 13 \}\]
. We can find this set by considering powers of 5 modulo 14.\[5^1 =5\equiv 5 \; (mod \; 14)\]
\[5^2=25 \equiv 11 \; (mod \; 14)\]
\[5^3=125 \equiv 13 \; (mod \; 14)\]
\[5^4=625 \equiv 9 \; (mod \; 14)\]
\[5^5 =3125 \equiv 3 \; (mod \; 14)\]
\[5^1=15625 \equiv 1 \; (mod \; 14)\]
