Question

3. For any positive integer a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy

Answer 1

Answer:

0,1,2

Step-by-step explanation:

a = 3q+r (Given)

b = 3 (Given)

According to the concept of Euclid’s division Lemma, every integer has a certain divisibility rule. It states that any positive integer say ‘a’ can be divided by any other positive integer say ‘ b’ in such a way that it will leave the remainder ‘r’. It further states that for any two positive integers ‘a’ and ‘b’ there exists two unique whole numbers say ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.

Where, a is the dividend, b is the divisor, q is the quotient and r is the remainder.

As per the question, since the integers are a and 3, thus  

Let the values that 'r’ can take = 0 ≤ r < 3.

Therefore, the possible values 'r’ will be 0,1,2.

Answer 2

Step-by-step explanation:

INTEGERS = A, 3

ASSUME A = 6

6 = 3Q + R

R = 6 - 3Q