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数论（一）

1.同余系统

1.1 最大公约数(Greatest common divisor)

',4)),Q("h4",r,[Q("a",o,[Q("span",null,[T[4]||(T[4]=l("1.1.1 ")),Q("mjx-container",H,[(t(),a("svg",h,T[0]||(T[0]=[m('',1)]))),T[1]||(T[1]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{"data-mjx-texclass":"OP",movablelimits:"true"},"gcd"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"x"),Q("mo",null,","),Q("mi",null,"y"),Q("mo",{stretchy:"false"},")")])],-1))]),T[5]||(T[5]=l("表示x和y的最大公约数，也叫最大公因数，例如")),Q("mjx-container",g,[(t(),a("svg",i,T[2]||(T[2]=[m('',1)]))),T[3]||(T[3]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{"data-mjx-texclass":"OP",movablelimits:"true"},"gcd"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"6"),Q("mo",null,","),Q("mn",null,"15"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"3")])],-1))])])])]),T[469]||(T[469]=Q("p",null,"欧几里得对“公约”的解释，给定两条长度不同的线段 a 和 b ，如果能够找到第三条线段 c ，它既可以度量 a ，又可以度量 b ，我们就说 a 和 b 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2.中国剩余定理

2.1 孙子算经中的问题

“今有物，不知其数。三、三数之，剩二；五、五数之，剩三；七、七数之，剩二。问物几何？答曰：二十三。”
《孙子算经》卷下第二十六问

2.2 数学解释

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用递归算法实现

pair<int,int> exgcd(int a,int b){
    if(b == 0)return make_pair(1,0);
    pair<int,int>temp = exgcd(b,a%b);
    pair<int,int>ans = make_pair(temp.second,temp.first-(int)(a/b)*temp.second);
    return ans;
}

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