[Template] Shu Pei Theorem

[Time Gate]

https://www.luogu.org/problemnew/show/P4549

[Problem-solving ideas]

Greatest common divisor of number theory + + indeterminate equation

Shu Pei content and brief proof of Theorem

ax + by = c Sufficient Conditions (xy is any integer) holds c is a multiple of gcd (a, b) of

Set S = gcd⁡ (A, B) , apparently S | A, and s|b

And because x, y∈Z *

So s|ax, s|by

Prior to making formula is clearly established, it must meet c is a and b multiple of the Convention

And because x and y are positive integers

Therefore c must be a, b, the common denominator

Therefore, the proof of the theorem was established

The same number can be more

【code】

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <algorithm>
 4 using namespace std;
 5 int n,k,ans;
 6 inline int gcd(int a,int b){
 7     if(b==0)return a;
 8     return gcd(b,a%b);
 9 }
10 int main(){
11     //freopen("4549.in","r",stdin);
12     //freopen("4549.out","w",stdout);
13     scanf("%d",&n);
14     for(register int i=1;i<=n;i++){
15         scanf("%d",&k);
16         if(k<0)k*=(-1);
17         ans= gcd(ans,k);
18     }
19     printf("%d\n",ans);
20     return 0;
21 }