Claim:The quotient and remainder are unique

From CS2800 wiki
For any [math]a \href{/cs2800/wiki/index.php/%E2%88%88}{∈} \href{/cs2800/wiki/index.php/%E2%84%A4}{ℤ} [/math] and [math]b \neq 0 \href{/cs2800/wiki/index.php/%E2%88%88}{∈} \href{/cs2800/wiki/index.php/%E2%84%A4}{ℤ} [/math], if [math]q [/math] and [math]r [/math] are a quotient and remainder of [math]a [/math] and [math]b [/math] (that is, if [math]a = qb + r [/math] and [math]0 \leq r \lt b [/math]), and if [math]q' [/math] and [math]r' [/math] are also a quotient and remainder of [math]a [/math] over [math]b [/math], then [math]q = q' [/math] and [math]r = r' [/math].