February+9

Question 1

How many solutions do the following congruences have? (there is no need to solve them)

a) math x^{17}\equiv 0 \mod 137 math

b) math x^7\equiv 15 \mod 137 math

c) math x^{17}\equiv 1 \mod 137 math

d) math x^{51}\equiv 1 \mod 137 math

Question 2

How many primitive roots are there modulo 19? Find all of them.