Dividing a certain number by $$3$$ leaves a remainder of $$1$$, dividing it by $$5$$ leaves a remainder of $$3$$, dividing it by $$7$$ leaves a remainder of $$5$$. Given that the number is between $$400$$ and $$500$$, what is its possible value? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem