Given any set , where we define two operations: and .
Modular Arithmetic is a binary operation. That is, a binary operation is where there are two inputs and one output.
Example in :
If and in , then and .
Example Modular Arithmetic table in :
Modular Arithmetic has several different types of properties.
We can further this by putting a congruence set to a power. Say . Jut as with exponents with integers, there are n number of being multiplied.
A Power Example
For we have .
Now for : . Every x in is a solution of .
Does there exist in such that ?
has no solution, yet , if $x=$,
Uses of Modular Arithmetic
Note: An analogous setting will reappear when looking at ‘rings’.