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Question 1
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
 


Solution

No, we cannot.
By Euclid's Lemma, b=aq+r, 0r<a [ dividend=divisor×quotient + remainder]
Here, b is any positive integer a=4,b=4q+r for 0r<=0,1,2,3
So, this must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3.

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