Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
No, we cannot express any positive integer as 4q + 2.
By Euclid's Lemma, a=bq+r, 0≤r<b [∵ dividend=divisor×quotient + remainder]
Here, a and b are any positive integers.
When we take b = 4, then, a=4q+r, 0≤r<4.
So, any integer must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3. Thus, not all integers can be expressed as 4q + 2.