Question

*Fill in the blank: Euclid’s division lemma states that for any positive integers a and b there exist unique integers q and r such that "a = bq + r", where r must satisfy _________.*

1️⃣ 1 < r < b
2️⃣ 0 < r ≤ b
3️⃣ 0 ≤ r < b
4️⃣ 0< r < b​

Answer 1

Answer:

3) 0 ≤ r < b

Step-by-step explanation:

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Answer 2

Answer: (3) 0 ≤ r < b

Explanation: Euclid's division lemma states that – "For any positive integers a and b there exist unique integers q and r such that "a = bq + r", where r must satisfy 0 ≤ r < b."

More:

If a number q is expressible interms of A^p, B^q, etc., i.e.,

$\rm q = A^p \cdot B^q \cdot C^r \cdot ...$,

then,

• Number of factors of q = $\rm (p + 1) \cdot (q + 1) \cdot (r + 1) \cdot (s + 1) \cdot ...$
• Sum of factors of q = $\rm \dfrac{A^{p + 1} - 1}{A - 1} \cdot \dfrac{B^{q + 1} - 1}{B - 1} \cdot ...$
• Product of factors of q = $\rm q^{(\dfrac{Total \ factors}{2})}$