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. By Euclid's Lemma, b=aq+r, 0≤r<a [∵ dividend=divisor×quotient + remainder] Here, b is any positive integer a=4,b=4q+r for 0≤r<=0,1,2,3 So, this must be in the form 4q, 4q + 1, 4q + 2 or 4q + 3.

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