Page "Division (mathematics)" Paragraph 33

The division algorithm is a mathematical theorem that precisely expresses the outcome of the usual process of division of integers.

In particular, the theorem asserts that integers called the quotient q and remainder r always exist and that they are uniquely determined by the dividend a and divisor d, with d ≠ 0.

Formally, the theorem is stated as follows: There exist unique integers q and r such that a = qd + r and 0 ≤ r < | d |, where | d | denotes the absolute value of d.