(a) Make addition and multiplication tables showing how integers are added and multiplied modulo 6.
Some entries are provided to get you started.
Table of values of m+n mod 6
Table of values of mn mod 6
m
m
0 1 2 3 4 5
0 1 2 3 4 5
n
n
0 0 1 2
0 0 0 0
1
1
2
2 2
3
1
3 3 0 3
4
1
4 0
5
5
(b) Use your tables to find two different solutions for $x$ in the congruence equation $2x \equiv 4 \pmod{6}$.
(c) How many solutions are there to $3x \equiv 3 \pmod{6}$ with $x \in \{0,1,2,3,4,5\}$?
(d) Explain why it is impossible to solve $3x \equiv 2 \pmod{6}$.
(e) For which values of $n \in \{0, 1, 2, 3, 4, 5\}$ is there exactly one solution for $x$ to the congruence $5x \equiv n$
$\pmod{6}$ with $x \in \{0,1,2,3,4,5\}$?
