When $$1001$$ is divided by a certain one-digit number, the remainder is $$5$$. What is the remainder when the same one-digit number divides $$2006$$? ． 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder
$$1001\div a=b~~\text {R} 5$$, $a$ is a one-digit number bigger than $$5$$, so $a$ =6;  $$1005\div a=c~ \text {R} 9$$;  $$2006\div a=d \text {R} 14$$;  $$14=2\times6 + 2$$, so the remainder is $$2$$. 