Question

Define Endid's division lemma with an example.

Answer 1

Endid's division lemma states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r. This lemma is used frequently in number theory and modular arithmetic.

Step-by-step explanation:

Endid's division lemma is a mathematical theorem that states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where q is the quotient and r is the remainder. This lemma is used frequently in number theory and modular arithmetic.

For example, let's consider the division of 17 by 3. In this case, a = 17 and b = 3. By applying Endid's division lemma, we can write 17 as 3q + r. The quotient q will be 5 and the remainder r will be 2. Therefore, 17 = 3(5) + 2.