Q. 13.9( 69 Votes )

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

Answer :

No


By Euclid’s Lemma,


b = a × q + r, 0 ≤ r < a [Using dividend = divisor × quotient + remainder]


Here, b is any positive integer.


According to the question, a = 4


b = 4q + r where 0 ≤ r < 4


r = 0, 1, 2, 3


So, this must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3.


Hence, every positive integer cannot be of the form 4q + 2.


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