 Euclidean division

For an integer $a$ and positive integer $b$, Euclidean division writes $a=bq+r$ with unique integer quotient $q$ and remainder $0\le r<b$. For $a\ge 0$, repeated quotient-and-remainder steps yield the digits of a base-p expansion when $b=p$. The uniqueness follows because the difference of two permitted remainders cannot be a nonzero multiple of $b$.

Euclidean division is a method of dividing two integers that results in a quotient and a remainder. It can be formally defined for any two integers \( a \) (the dividend) and \( b \) (the divisor), with \( b > 0 \).