For some integer q,every odd integer is of th | vedclass

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(D) By definition,an integer is even if it is divisible by $2$,which can be expressed as $2q$ for some integer $q$.An odd integer is an integer that i

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$2q+1$

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(D) By definition,an integer is even if it is divisible by $2$,which can be expressed as $2q$ for some integer $q$.An odd integer is an integer that is not divisible by $2$.When we divide any odd integer by $2$,the remainder is always $1$.According to Euclid's division lemma,any integer $a$ can be expressed as $a = bq + r$,where $0 \le r For $b = 2$,we have $a = 2q + r$,where $r = 0$ or $r = 1$.If $r = 0$,$a = 2q$ (even integer).If $r = 1$,$a = 2q + 1$ (odd integer).Therefore,every odd integer is of the form $2q + 1$ for some integer $q$.

For some integer $q$,every odd integer is of the form

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