Question

For any positive integers 'a' and 3, there exist unique integers 'q' and 'r' such that a = 3q + r, where r must satisfy:
1. 1 < r < 3
2. 0 < r < 3
3. 0 ≤  r < 3
4. 0 < r ≤ 3

Answer 1

Correct Answer - Option 3 : 0 ≤  r < 3

Concept:

Euclid's division lemma: It states that if 'a' and 'b' are positive integers then there exists 'q' and 'r' such that 

a = bq + r    where,  0 ≤ r < b

Calculation:

Here in the given problem, we have 'a' and 'b = 3' as any positive integers, then by applying the above lemma there exists 'q' and 'r' such that 

a = 3q +r where,

0 ≤  r < 3    ( As b = 3) 

Hence, the correct answer is 0 ≤  r < 3.