Write whether every positive integer can be o | vedclass

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(B) No,every positive integer cannot be of the form $4q + 2$.According to Euclid's Division Lemma,for any positive integer $b$ and a positive integer

Vedclass · Accepted Answer

No

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(B) No,every positive integer cannot be of the form $4q + 2$.According to Euclid's Division Lemma,for any positive integer $b$ and a positive integer $a = 4$,there exist unique integers $q$ and $r$ such that $b = 4q + r$,where $0 \le r This means the possible values for the remainder $r$ are $0, 1, 2,$ and $3$.Therefore,any positive integer $b$ can be expressed in one of the following forms: $4q, 4q + 1, 4q + 2,$ or $4q + 3$.Since a positive integer can also take the forms $4q, 4q + 1,$ or $4q + 3$,it is not restricted to only the form $4q + 2$.

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

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