2016年全国AMC六年级竞赛8第5题
$$N$$是一个两位数数字．当$N$除以$9$，余数为$1$.当$N$除以$10$，余数为$3$.当$N$除以$11$时，余数是多少?  The number $$N$$ is a two-digit number. When $$N$$ is divided by $$9$$, the remainder is$$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. $$What$$ is the remainder when $$N$$ is divided by $$11$$? 
拓展思维->能力->运算求解 Overseas Competition->知识点->数论模块->余数问题->中国剩余定理
翻译：$$N$$是一个两位数，$$N$$除以$$9$$余$$1$$，除以$$10$$ 余$$3$$，那么$$N$$除以$$11$$余．  $$N\div 9=\cdots \cdots 1$$，且个位是$$3$$，所以$$N=9\times 8+1=73$$（$$N$$是一个两位数），$$73\div 11=6\cdots \cdots 7$$． 