find all whole number solutions of the congruence equation x

find all whole number solutions of the congruence equation x 12 mod 5

Solution

x 12 mod 5 means (x-12) is divisible by 5

so we can write x-12=5m, where m is an integer

we are asked to use only whole numbers

and we know first whole number that is divisible by 5 is 0

so that means starting value of m is 0

hence x-12=5m, where m is an integer, m>=0

or x=12+5m, where m =0,1,2,3...