How do you complete a multiplication table in Zn Please give

Solution

Zn will have elements as {0,1,2,3....n-1}

The table for multipliction will be as follows:

Consider any two elements a,b in Zn

Multiply ab

And write ab if ab< n

If ab >n, write product as ab mod n

Hence product of two elements is defined as

ab = ab mod n.

Example:

Consider Z5

Z5 has elements as {0,1,2,3,4,5}

Leave the products less than or equal to 5 as it is

If more than 5, divide by 5, and write remainder. For example 16 = 5x3 +1

So replace 16 by 1, 20 by 0, and so on.