Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
No, we cannot.
By Euclid's Lemma, b=aq+r, 0≤r<a [∵ dividend=divisor×quotient + remainder]
Here, b is any positive integer a=4,b=4q+r for 0≤r<=0,1,2,3
So, this must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3.