Question

for any integer a and 5 , there exist a unique integer q and r , such that a= 5q+r . find the possible values of a and r

Answer 1

by Euclid division lemma
rcan be 1234
and a can be 123

Answer 2

According to question

integers = a and 5

And it is given that

a = 5q + r
Let 
q = 1
Thus
a = r + 5
Thus
Let r = 1
Thus   a= 5
and if a =1
r = 1-5 = -4