Question 1
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, we cannot express any positive integer as 4q + 2.
By Euclid's Lemma, $a = b q + r, 0 \leq r < b [∵ d i v i d e n d = d i v i s o r \times q u o t i e n t + r e m a i n d e r]$

Here, a and b are any positive integers.

When we take b = 4, then, $a = 4 q + r, 0 \leq r < 4$ .

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.

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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.

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