Question

write whether every positive integer can be of the form 4q+2 , where q is an integer . justify your answer

Answer 1

Let a be a given positive number.

On dividing a by 4, let q be the quotient and r be the remainder.

Then,by Euclid's algorithm,we have:

a=4q+r where 0<=r<4

a=4q+r where r=0,1,2,3

a=4q+2=2(2q+1)

It is clearly shown that 2q+1 is divisible by 2.

Therefore,4q+2 is a positive integer.

Answer 2

Answer:

4q+2 is a negative integer

Step-by-step explanation:

q=-1

4(-1)+2

-4+2

-2