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

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

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Solution:
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.​