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For any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a = b × q + r$ where $0 ≤ r < b$ states

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Fundamental Theorem of Arithmetic

Euclid’s lemma

Euclidean Distance

Ceva’s theorem

answer is B.

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Detailed Solution

Given a statement that for any two positive integers

a

and

b

we can find two whole numbers

q

and

r

such that

a = b × q + r

where

0 ≤ r < b

.
Definition of Euclid's Division Lemma. A lemma is a proven statement used for proving another statement.
A lemma is a proven statement used for proving another statement.
According to Euclid's Division Lemma, if we have two positive integers

a

and

b

, then there would be whole numbers

q

and

r

that satisfy the equation

a = b q + r

, where

0 ≤ r < b

a

is the dividend.

b

is the divisor.
Euclid's division lemma, states that for any two positive integers

a

and

b

we can find two whole numbers

q

and

r

such that

a = b × q + r

where

0 ≤ r < b .

Hence, it states the Euclid’s Division Lemma.
So, the correct option is 2.

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