Question

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

Answer 1

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