Write whether every positive integer can be of the form 4q + 2, where

1.	Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
Answer» No, every positive integer cannot be of the form 4q + 2, where q is an integer. Justification: All the numbers of the form 4q + 2, where ‘q’ is an integer, are even numbers which are not divisible by ‘4’. For example, When q=1, 4q+2 = 4(1) + 2= 6. When q=2, 4q+2 = 4(2) + 2= 10 When q=0, 4q+2 = 4(0) + 2= 2 and so on. So, any number which is of the form 4q+2 will give only even numbers which are not multiples of 4. Hence, every positive integer cannot be written in the form 4q+2

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

Answer»

No, every positive integer cannot be of the form 4q + 2, where q is an integer.

Justification:

All the numbers of the form 4q + 2, where ‘q’ is an integer, are even numbers which are not divisible by ‘4’.

For example,

When q=1,

4q+2 = 4(1) + 2= 6.

When q=2,

4q+2 = 4(2) + 2= 10

When q=0,

4q+2 = 4(0) + 2= 2 and so on.

So, any number which is of the form 4q+2 will give only even numbers which are not multiples of 4.

Hence, every positive integer cannot be written in the form 4q+2