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For any positive integers 'p' and 9, there exist unique integers 'a' and 'b' such that p = 9a + b, where b must satisfy:

For any positive integers 'p' and 9, there exist unique integers 'a' and 'b' such that p = 9a + b, where b must satisfy: Correct Answer 0 ≤  b < 9  

Concept:

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

p = aq + b    where,  0 ≤ b < q

Calculation:

Here in the given problem, we have 'p', and 'q' = 9 as any positive integers, then by applying the above lemma there exists 'a' and 'b' such that

p = 9q + b where,

0 ≤ b < 9 ( As q = 9)

Hence, the correct answer is 0 ≤  b < 9.  

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