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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 express any positive integer as 4q + 2.
By Euclid's Lemma, a=bq+r, 0r<b [ dividend=divisor×quotient + remainder]

Here, a and b are any positive integers.

When we take b = 4, then, a=4q+r, 0r<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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