Question

Write out a table of discrete logarithms modulo 17 with respect to the primitive root 3.

Short answer

$\begin{array}{r}{\log }_{3}1=0\\ {\log }_{3}2=15\\ {\log }_{3}3=1\\ {\log }_{3}4=12\\ {\log }_{3}5=5\\ {\log }_{3}6=15\\ {\log }_{3}7=11\\ {\log }_{3}8=10\\ {\log }_{3}9=2\\ {\log }_{3}10=3\\ {\log }_{3}11=7\\ {\log }_{3}12=13\\ {\log }_{3}13=4\\ {\log }_{3}14=9\\ {\log }_{3}15=6\\ {\log }_{3}16=8\end{array}$

Step-by-step solution

Step: 1

$\begin{array}{r}{\log }_{3}1=0\\ {\log }_{3}2=15\\ {\log }_{3}3=1\\ {\log }_{3}4=12\\ {\log }_{3}5=5\\ {\log }_{3}6=15\\ {\log }_{3}7=11\\ {\log }_{3}8=10\\ {\log }_{3}9=2\\ {\log }_{3}10=3\\ {\log }_{3}11=7\\ {\log }_{3}12=13\\ {\log }_{3}13=4\\ {\log }_{3}14=9\\ {\log }_{3}15=6\\ {\log }_{3}16=8\end{array}$