Question

write whether every positive integer can be of the form 4 Q + 2 where q
is some integer justify your answer

Answer 1

Let the positive integer be 'a'
And, another number 'b' where b = 4
By remainder theorem :-
a = 4q+r
Where q is some integer and r is the remainder and the condition added is 0 ≤ r < 4

.•. r can be 0,1,2 and 3

If r = 0
.•. a = 4q
.•. for r = 0, a is even as any number multiplied with any even number gives even number
.•. for r = 1 and 3, a will be odd as 4q is even and even + odd = odd
.•. for r = 2, a is even
.•. a = 4q + 2 is even
So, we conclude that any positive integer is in the form 4q + 2.

Hope you can understand my answer.