Write whether every positive integer can be of the form 4q + 2, w… - Vidyadip

Question

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

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Answer

'No'. By Euclid's division lemma, we have
dividend = divisor × quotient + remainder
a = bq + r
Let b = 4 then
a = 4q + r where q, r are positive
Since $0\leq\text{r}<4\therefore\text{ r}=0,1,2,3$
So, a become of the form, 4q, 4q + 1, 4q + 2 and 4q + 3
So, all integers can be3 represented by all 4q, 4q + 1, 4q + 2, and 4q + 3 not only by 4q + 2.

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