Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form `2q+1`, where q is some integer.

Explanation

Let `a and b` are two positive integers such that, `a>b`.

Then, for any interger `q`, we can write,

`a = bq+r`

Here, ` r` is remainder that we get after dividing `a` by `b`.

Now, if `b =2`, then,

`a=2q+r`

For every positive even number, `r=0`. Thus,

`a = 2q`

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