#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define sfc(a) scanf("%c",&a)
#define pii pair<int,int>
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define pii pair<int,int>
#define ff first
#define ss second
#define sz(x) x.size()
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define for0(i,n) for(int i=0;i<n;i++)
#define for1(i,n) for(int i=1;i<=n;i++)
#define forrev(i,n) for(int i=n-1; i>=0; i--)
#define forab(i,a,b) for(int i=a;i<=b;i++)
#define forba(i,b,a) for(int i=b;i>=a;i--)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI acos(-1) //3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<row && ty>=0 && ty<col
#define intlim 2147483648
#define MAX 10000007
#define inf 100000008
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
int main()
{
//CIN;
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
int t,a,c,b;
sf(t);
for1(z,t)
{
sff(a,c);
if(c%a==0)
{
int b=c/a,i;
for(i=b;i<=MAX;i+=b)
{
if(lcm(a,i)==c) break;
}
pf("%d\n",i);
}
else pf("NO SOLUTION\n");
}
return 0;
}
Category Number Theory
UVa – 10948 – The primary problem
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(i,a,b) for(int i=a;i<=b;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
bool p[MAX+2];
vector<int>prime;
void sieve()
{
p[0]=p[1]=1;
int root=sqrt(MAX);
for(int i=2; i<=root; i++)
{
if(p[i]==0)
{
for(int j=i*i; j<=MAX; j+=i)
{
p[j]=1;
if(i%2==1) j+=i;
}
}
}
for(int i=2; i<=MAX; i++)
{
if(p[i]==0) prime.push_back(i);
}
}
int c=0;
void gold(int n)
{
for(int i=0; prime[i]<=n/2; i++)
{
int a=n-prime[i];
if(p[a]==0)
{
c=1;
pf("%d+%d\n",prime[i],a);
break;
}
}
}
int main()
{
//CIN;
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
sieve();
int n;
while(sf(n)==1 && n!=0)
{
c=0;
pf("%d:\n",n);
if(n==4)
{
pf("2+2\n");
continue;
}
gold(n);
if(c==0) pf("NO WAY!\n");
}
return 0;
}
UVa – 686 – Goldbach’s Conjecture (II)
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(i,a,b) for(int i=a;i<=b;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 32770
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
bool p[MAX];
void sieve()
{
p[0]=p[1]=1;
int root=sqrt(MAX);
for(int i=2; i<=root; i++)
{
if(p[i]==0)
{
for(int j=i*i; j<=MAX; j+=i)
{
p[j]=1;
if(i%2!=0) j+=i;
}
}
}
}
int gold(int n)
{
if(n==4) return 1;
int i,j,pairs=0;
for(i=3; i<=n/2; i+=2)
{
if(p[i]==0)
{
int a=n-i;
if(p[a]==0) pairs++;
}
}
return pairs;
}
int main()
{
//CIN;
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
sieve();
int n;
while(sf(n) && n!=0)
{
pf("%d\n",gold(n));
}
return 0;
}
UVa – 543 – Goldbach’s Conjecture
#include <bits/stdc++.h>
#define pf printf
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d) scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d) scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e) scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b) memset(a,b,sizeof(a))
#define pb(a) push_back(a)
#define pbp(a,b) push_back({a,b})
#define db double
#define ft float
#define ll long long
#define ull unsigned long long
#define ff first
#define ss second
#define sz(x) x.size()
#define qu queue
#define pqu priority_queue
#define vc vector
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define all(x) x.begin(),x.end()
#define CIN ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c) max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c) min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define loopab(i,a,b) for(int i=a;i<=b;i++)
#define stlloop(x) for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
#define case1(z) cout<<"Case "<<z<<": "
#define case2(z) printf("Case %d: ",z)
#define PI 3.14159265358979323846264338328
#define valid(tx,ty) tx>=0 && tx<r && ty>=0 && ty<c
#define intlim 2147483648
#define MAX 1000000
#define inf 10000000
/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*---------------------------------------------------------------------*/
using namespace std;
bool p[MAX];
void sieve()
{
p[0]=p[1]=1;
int root=sqrt(MAX);
for(int i=2; i<=root; i++)
{
if(p[i]==0)
{
for(int j=i*i; j<=MAX; j+=i)
{
p[j]=1;
if(i%2!=0) j+=i;
}
}
}
}
int gold(int n)
{
int i,j;
for(i=3; i<=n/2; i+=2)
{
if(p[i]==0)
{
int a=n-i;
if(p[a]==0)
{
pf(" %d + %d\n",i,a);
break;
}
}
}
}
int main()
{
//CIN;
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
sieve();
int n;
while(sf(n)==1 && n!=0)
{
pf("%d =",n);
gold(n);
}
return 0;
}
UVa – 11466 – Largest prime divisors
#include <bits/stdc++.h>
using namespace std;
bool p[40000000];
vector<long long> prime;
void sieve(long long n)
{
p[0]=p[1]=1;
for(long long i=2; i<n;)
{
prime.push_back(i);
for(long long j=i*i; j<n; j+=i)
{
p[j]=1;
}
for(++i;; i++)
{
if(!p[i]) break;
}
}
}
int main()
{
//freopen("in.txt","r",stdin);
long long i,c,d,n;
sieve(35000000);
while(cin>>n)
{
if(n==0)
{
break;
}
c=0;
d=0;
n=abs(n);
for(i=0; i<prime.size() && prime[i]*prime[i]<=n; i++)
{
if(n%prime[i]==0)
{
c++;
d=max(d,prime[i]);
while(n%prime[i]==0)
{
n/=prime[i];
}
}
}
if(n>1)
{
d=max(d,n);
c++;
}
if(c<=1)
{
cout<<"-1"<<endl;
}
else
{
cout<<d<<endl;
}
}
return 0;
}
Fall out, Codes! 