Before starting to do any work, can we apply some intuition? The equation is “mod 4” meaning “all numbers should be converted to their remainder when divided by 4”. In other words, we use the following equivalences when dealing with any numbers:
0 = 4 = 8 = …,
1 = 5 = 9 = …,
2 = 6 = 10 = …,
3 = 7 = 11 = ….
The above equivalences are true in the mod-4 universe, because two numbers that differ by 4 will have the same remainder when divided by 4 (proving this will be a good exercise).
The question refers to 7, which in the mod-4 universe is the same as 3. So we can rewrite the question as 3=3(4)
3
x
=
3
(
m
o
d
4
)
, which makes the answer a lot more obvious: =1(4)
x
=
1
(
m
o
d
4
)
is a solution to this equation.
