Chapter 4.4, Problem 57E

Write out a table of discrete logarithms modulo 17 with respect to the primitive root3.

If m is a positive integer, the integer a is a quadratic residue of m if $\text{gcd}\left(a,m\right)=\text{1}$ and the congruence $x^2\equiv a(\mathrm{mod}m)$ has a solution. In other words, a quadratic residue of m is an integer relatively prime to m that is a perfect square modulo m. If a is not a quadratic residue of m and $\gcd (a,m)=1$ , we say that it is a quadratic nonresidue of m. For example, 2 is a quadratic residue of 7 because $\text{gcd}\left(\text{2},\text{7}\right)=\text{1}$ and ${\text{3}}^{\text{2}}\equiv \text{2}\left(\text{mod 7}\right)$ and 3 is a quadratic nonresidue of 7 because $\text{gcd}\left(\text{3},\text{7}\right)=\text{1}$ and $x^{\text{2}}\equiv 3\left(\text{mod 7}\right)$ has no solution.