中国剩余定理

标签：中国剩余定理   欧几里得算法   

program t;
var n,i:longint;
    j,k,m,x,y,ans,m1:int64;
    a,b:array[1..10]of int64;
procedure gcd(a,b:int64;var x,y:int64);
var t:int64;
begin
 if b=0 then
  begin
   x:=1;y:=0;exit;
  end;
 gcd(b,a mod b,x,y);
 t:=x;x:=y;
 y:=t-(a div b)*y;
end;
begin
 read(n);
 for i:=1 to n do
  begin
   read(j,k);
   a[i]:=int64(j);
   b[i]:=int64(k);
  end;
 m:=1;
 for i:=1 to n do
  m:=m*a[i];
 for i:=1 to n do
  begin
   m1:=m div a[i];
   gcd(m1,a[i],x,y);//ti*Mi≡1 mod mi
   ans:=(ans+(b[i]*x mod m)*m1 mod m)mod m;
  end;
 while ans<0 do ans:=ans+m;
 write(ans);
end.

x≡1 mod 5

x≡2 mod 7

中国剩余定理

标签：中国剩余定理   欧几里得算法   

原文地址：http://blog.csdn.net/zz_ylolita/article/details/41788977