please explain this mcq- According to Euclid's division of Lemma, for a and 5 if a=5q+r is unique then r = ...... is not possible.

Question

A. 0
B. 2
C. 4
D. 6

Answer 1

The Lemma says that for any pair, a,b we can find q,r such that

a = bq+r

The above equation is just

a ≡ r (mod 5)

There is no unique value of a which will determine r.