Reference no: EM131570137

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

If m is a positive integer, the integer a is a quadratic residue of m if gcd(a, m) = 1 and the congruence x2 ≡ a (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 gcd(2, 7) = 1 and 32 ≡ 2 (mod 7) and 3 is a quadratic nonresidue of 7 because gcd(3, 7) = 1 and x2 ≡ 3 (mod 7) has no solution.