Question

Question 1
For some integer m, every even integer is of the form

A) m
B) m + 1
C) 2m
D) 2m + 1

Answer 1

We know that the even integers are divisible by 2.

If we take any integer, say a, as the dividend and 2 as the divisor, then by Euclid's division lemma

$a=2m+r$ Where $m$ is the quotient and $0\le r<2$

If a is an even integer, then the possible values of r are just 0.

If a is an odd integer, the possible values of r are just 1.

Thus, any even integer can be expressed as $2m$.

Hence, answer option is C.