Number Theory – Page 5 – Live with passion

12765

Asif NaeemAugust 18, 2014

[highlight]Solution:[/highlight]

#include <iostream>

using namespace std;

int a[10][10];
int ans1[8];
int ans2[8];

int main()
{
int N,M,n;
a[1][1]=1;
a[2][2]=1;
a[3][3]=1;
a[4][2]=2;
a[5][5]=1;
a[6][2]=1;
a[6][3]=1;
a[7][7]=1;
a[8][2]=3;
a[9][3]=2;

for(int i=1;i<=9;i++)
{
for(int j=1;j<=7;j++)
a[i][j]+=a[i-1][j];
}

//for(int i=1;i<=9;i++)
//cout<<a[9][i]<<" ";
while(cin>>N)
{
cin>>M;

if(N==0 && M==0)
break;

for(int i=1;i<8;i++)
{
ans1[i]=0;
ans2[i]=0;
}
for(int i=0;i<N;i++)
{
cin>>n;

if(n!=0)
for(int j=1;j<=7;j++)
ans1[j]+=a[n][j];

}

for(int i=0;i<M;i++)
{
cin>>n;

if(n!=0)
for(int j=1;j<=7;j++)
ans2[j]+=a[n][j];

}

int f=0;
for(int i=2;i<8;i++)
{
if(ans1[i]!=ans2[i])
{
cout<<"NO\n";
f=1;
break;
}
}

if(f==0)
cout<<"YES\n";
}

return 0;
}

#include <iostream>

using namespace std;

int a[10][10];

int ans1[8];

int ans2[8];

int main()

{

int N,M,n;

a[1][1]=1;

a[2][2]=1;

a[3][3]=1;

a[4][2]=2;

a[5][5]=1;

a[6][2]=1;

a[6][3]=1;

a[7][7]=1;

a[8][2]=3;

a[9][3]=2;

for(int i=1;i<=9;i++)

{

for(int j=1;j<=7;j++)

a[i][j]+=a[i-1][j];

}

//for(int i=1;i<=9;i++)

//cout<<a[9][i]<<" ";

while(cin>>N)

{

cin>>M;

if(N==0 && M==0)

break;

for(int i=1;i<8;i++)

{

ans1[i]=0;

ans2[i]=0;

}

for(int i=0;i<N;i++)

{

cin>>n;

if(n!=0)

for(int j=1;j<=7;j++)

ans1[j]+=a[n][j];

}

for(int i=0;i<M;i++)

{

cin>>n;

if(n!=0)

for(int j=1;j<=7;j++)

ans2[j]+=a[n][j];

}

int f=0;

for(int i=2;i<8;i++)

{

if(ans1[i]!=ans2[i])

{

cout<<"NO\n";

f=1;

break;

}

if(f==0)

cout<<"YES\n";

}

return 0;

}

12665

Asif NaeemAugust 17, 2014

#include <iostream>

using namespace std;

int main()
{
int a,b;
unsigned long long t;
int cnt,c=0;
while(cin>>a)
{
cin>>b;
int tmp=min(1001,b);
c++;
cnt=0;
for(int i=a;i<=tmp;i++)
{
for(int j=a;j<=tmp;j++)
{
t=(i*i*i)+(j*j*j);

if(t/10>b || t/10<a)
continue;

if(t%10==3)
cnt++;
}
}

cout<<"Case "<<c<<": "<<cnt<<"\n";

}

return 0;
}

#include <iostream>

using namespace std;

int main()

{

int a,b;

unsigned long long t;

int cnt,c=0;

while(cin>>a)

{

cin>>b;

int tmp=min(1001,b);

c++;

cnt=0;

for(int i=a;i<=tmp;i++)

{

for(int j=a;j<=tmp;j++)

{

t=(i*i*i)+(j*j*j);

if(t/10>b || t/10<a)

continue;

if(t%10==3)

cnt++;

}

cout<<"Case "<<c<<": "<<cnt<<"\n";

}

return 0;

}

12620

Asif NaeemAugust 15, 2014

#include <iostream>

using namespace std;

#define M 301

int F[M];

int main()
{
unsigned long long n,m,s;
int t,a,b;
int a1,b1;
int sum=0;
F[1]=1;
F[2]=1;
F[3]=2;

for(int i=4;i<M;i++)
{
F[i]=(F[i-1]+F[i-2])%100;
}

//cout<<F[296]<<" "<<F[297]<<" "<<F[298]<<" "<<F[299]<<" "<<F[300]<<" "<<F[301]<<" "<<F[302]<<"\n";
for(int i=1;i<M;i++)
{
sum+=F[i];
}

//cout<<sum<<"\n";
cin>>t;

while(t--)
{
cin>>n>>m;
a=n%300;
//a1=n/300;
b=m%300 ;
//b1=m/300;
s=0;
unsigned long long j,p;
for(unsigned long long i=n;i<=m;i++)
{
if(i%300==0)
{
s+=F[300];
j=i;
break;
}
s+=F[i%300];
if(i==m)
j=m;
}
if(j==m)
{
cout<<s<<"\n";
continue;
}

p=m-j;
s+=((p/300)*sum);

j=j+(p/300)*300;

for(unsigned long long i=j+1;i<=m;i++)
{
if(i%300==0)
{
s+=F[300];
j=i;
break;
}
s+=F[i%300];
}

cout<<s<<"\n";
}

return 0;
}

#include <iostream>

using namespace std;

#define M 301

int F[M];

int main()

{

unsigned long long n,m,s;

int t,a,b;

int a1,b1;

int sum=0;

F[1]=1;

F[2]=1;

F[3]=2;

for(int i=4;i<M;i++)

{

F[i]=(F[i-1]+F[i-2])%100;

}

//cout<<F[296]<<" "<<F[297]<<" "<<F[298]<<" "<<F[299]<<" "<<F[300]<<" "<<F[301]<<" "<<F[302]<<"\n";

for(int i=1;i<M;i++)

{

sum+=F[i];

}

//cout<<sum<<"\n";

cin>>t;

while(t--)

{

cin>>n>>m;

a=n%300;

//a1=n/300;

b=m%300 ;

//b1=m/300;

s=0;

unsigned long long j,p;

for(unsigned long long i=n;i<=m;i++)

{

if(i%300==0)

{

s+=F[300];

j=i;

break;

}

s+=F[i%300];

if(i==m)

j=m;

}

if(j==m)

{

cout<<s<<"\n";

continue;

}

p=m-j;

s+=((p/300)*sum);

j=j+(p/300)*300;

for(unsigned long long i=j+1;i<=m;i++)

{

if(i%300==0)

{

s+=F[300];

j=i;

break;

}

s+=F[i%300];

}

cout<<s<<"\n";

}

return 0;

}

12708

Asif NaeemAugust 11, 2014

#include <iostream>

using namespace std;

int main()
{
int t;
unsigned long long n;

cin>>t;

while(t--)
{
cin>>n;
cout<<n/2<<"\n";

}

return 0;
}

#include <iostream>

using namespace std;

int main()

{

int t;

unsigned long long n;

cin>>t;

while(t--)

{

cin>>n;

cout<<n/2<<"\n";

}

return 0;

}

10042

Asif NaeemAugust 11, 2014

#include <iostream>

#include <string>
#include <vector>
#include <string.h>

using namespace std;

int prime[1000001];
vector <long long> vb;

long long sumof(long long a)
{
long long l=0;
while(a)
{
l+=a%10;
a/=10;
}
return l;
}

int isPrime(long long n)
{
if(n<1000001)
{
if(prime[n]==0)
return 1;
else
return 0;
}
for(int i=2;i*i<=n;i++)
if(n%i==0)
return 0;

return 1;
}
int factorsum(long long n)
{
if(n<1000001)
{
if(prime[n]==0)
return 1;
}

long long tmp=0;
long long org=n;
while(n)
{
int f=0;
for(int i=0;i<vb.size();i++)
{
if(vb[i]>n)
{
f=0;
break;
}
if(n%vb[i]==0)
{
tmp+=sumof(vb[i]);
n/=vb[i];
f=1;
break;
}
}
if(f==0)
{
if(isPrime(n)==1 && n!=org)
tmp+=sumof(n);
break;
}
}
//cout<<tmp<<" ds\n";
if(tmp==0)
return 1;
if(tmp==sumof(org))
return 0;

return 1;
}

int main()
{
prime[0]=1;
prime[1]=1;

for(int i=4;i<1000001;i+=2)
{
prime[i]=1;
}

for(int i=3;i*i<1000001;i+=2)
{
if(prime[i]==0)
{
for(int j=i+i;j<1000001;j+=i)
prime[j]=1;
}
}
//vb.clear();
vb.push_back(2);
for(int i=3;i<1000001;i+=2)
{
if(prime[i]==0)
vb.push_back(i);
}

int t;
long long n;
//cout<<vb[vb.size()-1]<<"\n";
//cout<<isPrime(1000000007)<<"\n";
//cout<<factorsum(1000000007)<<"\n";
//cout<<prime[45495]<<"\n";
//cout<<sumof(456502);
cin>>t;

while(t--)
{
cin>>n;
n++;
while(factorsum(n))
{
n++;
}
cout<<n<<"\n";
}

//getchar();
return 0;
}

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#include <iostream>

#include <string>

#include <vector>

#include <string.h>

using namespace std;

int prime[1000001];

vector <long long> vb;

long long sumof(long long a)

{

long long l=0;

while(a)

{

l+=a%10;

a/=10;

}

return l;

}

int isPrime(long long n)

{

if(n<1000001)

{

if(prime[n]==0)

return 1;

else

return 0;

}

for(int i=2;i*i<=n;i++)

if(n%i==0)

return 0;

return 1;

}

int factorsum(long long n)

{

if(n<1000001)

{

if(prime[n]==0)

return 1;

}

long long tmp=0;

long long org=n;

while(n)

{

int f=0;

for(int i=0;i<vb.size();i++)

{

if(vb[i]>n)

{

f=0;

break;

}

if(n%vb[i]==0)

{

tmp+=sumof(vb[i]);

n/=vb[i];

f=1;

break;

}

if(f==0)

{

if(isPrime(n)==1 && n!=org)

tmp+=sumof(n);

break;

}

//cout<<tmp<<" ds\n";

if(tmp==0)

return 1;

if(tmp==sumof(org))

return 0;

return 1;

}

int main()

{

prime[0]=1;

prime[1]=1;

for(int i=4;i<1000001;i+=2)

{

prime[i]=1;

}

for(int i=3;i*i<1000001;i+=2)

{

if(prime[i]==0)

{

for(int j=i+i;j<1000001;j+=i)

prime[j]=1;

}

//vb.clear();

vb.push_back(2);

for(int i=3;i<1000001;i+=2)

{

if(prime[i]==0)

vb.push_back(i);

}

int t;

long long n;

//cout<<vb[vb.size()-1]<<"\n";

//cout<<isPrime(1000000007)<<"\n";

//cout<<factorsum(1000000007)<<"\n";

//cout<<prime[45495]<<"\n";

//cout<<sumof(456502);

cin>>t;

while(t--)

{

cin>>n;

n++;

while(factorsum(n))

{

n++;

}

cout<<n<<"\n";

}

//getchar();

return 0;

}

Category: Number Theory

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