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

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Given :

The given positive integer is $q$.

To do :

We have to find whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.

Solution :

By Euclid\'s division lemma,

If a and b are two positive integers, then,

$a = b q + r$, where $0 \leq r < b$

Here, $b$ is any positive integer

$a = 4, b = 4q + r$ for $0 \leq r < b$  [$r = 0,1,2, 3$]

Therefore,

This must be in the form $4q, 4q + 1, 4q + 2$ or $4q + 3$.

Updated on 10-Oct-2022 13:27:06