https://codeforces.com/contest/1152/problem/C
a和b,找到k,使得lcm(a+k,b+k)最小(a,b:1e9)
- 设gcd=gcd(a+k,b+k)且\(a<b\),即(a+k)%gcd=0,(b+k)%gcd=0,(a+k)%gcd=(b+k)%gcd,a%gcd=b%gcd
- 移项得b%gcd-a%gcd=0,(b-a)%gcd=0
- 枚举b-a的因数即gcd,维护最小值
#include<bits/stdc++.h> #define ll long long using namespace std; ll a,b,ans,ansk,k,tp,x; int main(){ scanf("%lld%lld",&a,&b); if(a>b)swap(a,b); ans=a/__gcd(a,b)*b; ansk=0; for(ll i=1;i*i<=(b-a);i++){ //cout<<i<<endl; if((b-a)%i)continue; x=i; if(a%x!=b%x)continue; if(a%x){ k=x-a%x; tp=(a+k)/__gcd(a+k,b+k)*(b+k); if(tp<ans){ ans=tp;ansk=k; }else if(tp==ans&&k<ansk){ ansk=k; } } x=(b-a)/i; if(a%x!=b%x)continue; if(a%x){ k=x-a%x; tp=(a+k)/__gcd(a+k,b+k)*(b+k); if(tp<ans){ ans=tp;ansk=k; }else if(tp==ans&&k<ansk){ ansk=k; } } } printf("%lld",ansk); }