Question

1. 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 only of the form 4q + 2.


Justification: Let a be any positive integer.


Then by Euclid’s division lemma, we have a = bq + r, where 0 ≤ r < b



Putting b = 4, we get a = 4q + r,


where 0 ≤ r < 4 Hence, a positive integer can be of the form, 4q, 4q + 1, 4q + 2 and 4q + 3.