Describe the partition of Z resulting from the equivalence r

Describe the partition of Z resulting from the equivalence relation = (mod 4).

Solution

a=b mod 4

implies and b give the same remainder modulo 4

There are only 4 least residues modulo 4: 0,1,2,3

So total 4 equivalence classes

The partitions are

[0]= Multiples of 4

[1]=INtegers of the form 4k+1

[2]=Integers of the form 4k+2

[3]=Integers of the form 4k+3