If `` a '' and `` d '' are integers , with `` d '' non-zero , it can be proven that there exist unique integers `` q '' and `` r '' , such that `` a '' = `` qd '' + `` r '' and 0 ≤ `` r '' < '' | d | '' .
If `` a '' and `` d '' are natural numbers , with `` d '' non-zero , it can be proved that there exist unique integers `` q '' and `` r '' , such that `` a '' = `` qd '' + `` r '' and 0 ≤ `` r '' < `` d '' .