Question

# 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, 0≤r<b [∵ dividend=divisor×quotient + remainder] Here, a and b are any positive integers. When we take b = 4, then, a=4q+r, 0≤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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