Determine all of the congruence classes for the relation of

Determine all of the congruence classes for the relation of congruence modulo 5 on the set of integers.

Solution

There are 5 least residues modulo 5 namely: 0,1,2,3,4

So there are 5 congruence classes corresponding to each residue

[0]= All multiples of 5

[1]=Integers of the form:5k+1

[2]=Integers of the form:5k+2

[3]=Integers of the form:5k+3

[4]=Integesr of the form:5k+4