Number Theory – Page 4 – Live with passion

516

Asif NaeemNovember 8, 2014

#include <iostream>
#include <math.h>
#include <vector>
#include <map>
#include <sstream>

using namespace std;

struct NODE{
       int cnt;
       //map<int,int> freq;
       vector<int> num;
       int freq[35];
}node[33000];
int prime[33000];
vector<int> v;

stringstream s;

int _pow(int a,int p)
{
    if(p==0)
    return 1;
    return a*_pow(a,p-1);
}

int factorize()
{
    int tmp,index;
    int prev=-1;
    int counter=0;
    for(int i=3;i<33000;i++)
    {
       prev=-1;
       counter=0;
       if(prime[i]==0 && i%2!=0)
       {
           if(prev==i)
           {
             node[i].freq[counter-1]++;
           }
           else
           {
               prev=i;
               node[i].freq[counter++]++;
               node[i].num.push_back(prev);
           }
           //node[i].freq[i]++;
           continue;
       }
       tmp=i;
       index=0;
       while(tmp>=(v[index]*v[index]))
       {
           if(tmp%v[index]==0)
           {
              tmp/=v[index];
              if(prev==v[index])
              {
                 node[i].freq[counter-1]++;
              }
              else
              {
                  prev = v[index];
                  node[i].freq[counter++]++;
                  node[i].num.push_back(prev);
              }
              //node[i].freq[v[index]]++;
              index=-1;
           }
           index+=1;
       }
       if(tmp>1)
       {
          if(prev==tmp)
          {
             node[i].freq[counter-1]++;
          }
          else
          {
              prev=tmp;
              node[i].freq[counter++]++;
              node[i].num.push_back(prev);
          }

          //node[i].freq[tmp]++;
       }
       node[i].cnt=counter;
    }

   return 0;
}
int main()
{
    string str;
    double p = sqrt(33000)+4;

    for(int i=3;i<p;i+=2)
    {
        if(prime[i]==0)
        {
            for(int j=i+i;j<33000;j+=i)
            prime[j]=1;

        }
    }
    v.clear();
    v.push_back(2);

    for(int j=3;j<33000;j++)
    {
       if(prime[j]==0 && j%2!=0)
       v.push_back(j);
    }

    factorize();
    int n,numb;
    int a,b;
    while(1)
    {
       getline(cin,str);
       if(str=="0")
       break;
       istringstream s(str);
       int c=0;
       numb=1;
       while(s>>n)
       {
         if(c==0)
         {
            a=n;
            c=1;
         }
         else if(c)
         {
            b=n;
            c=0;

            numb*=_pow(a,b);
         }
       }
       NODE tNode = node[numb-1];
       //cout<<tNode.num.size()<<"\n";
       //cout<<tNode.num[5]<<" "<<tNode.freq[5]<<"\n";
       //for(int i=node[numb-1].num.size()-1;i>=0;i++)
       for(int i=(tNode.num.size()-1);i>=0;i--)
       {
          cout<<tNode.num[i]<<" ";//cout<<ii->first<<" "<<ii->second<<" ";
          if(i)
          cout<<tNode.freq[i]<<" ";
          else
          cout<<tNode.freq[i]<<"\n";

       }
    }

    return 0;
}

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

#include <iostream>

#include <math.h>

#include <vector>

#include <map>

#include <sstream>

using namespace std;

struct NODE{

int cnt;

//map<int,int> freq;

vector<int> num;

int freq[35];

}node[33000];

int prime[33000];

vector<int> v;

stringstream s;

int _pow(int a,int p)

{

if(p==0)

return 1;

return a*_pow(a,p-1);

}

int factorize()

{

int tmp,index;

int prev=-1;

int counter=0;

for(int i=3;i<33000;i++)

{

prev=-1;

counter=0;

if(prime[i]==0 && i%2!=0)

{

if(prev==i)

{

node[i].freq[counter-1]++;

}

else

{

prev=i;

node[i].freq[counter++]++;

node[i].num.push_back(prev);

}

//node[i].freq[i]++;

continue;

}

tmp=i;

index=0;

while(tmp>=(v[index]*v[index]))

{

if(tmp%v[index]==0)

{

tmp/=v[index];

if(prev==v[index])

{

node[i].freq[counter-1]++;

}

else

{

prev = v[index];

node[i].freq[counter++]++;

node[i].num.push_back(prev);

}

//node[i].freq[v[index]]++;

index=-1;

}

index+=1;

}

if(tmp>1)

{

if(prev==tmp)

{

node[i].freq[counter-1]++;

}

else

{

prev=tmp;

node[i].freq[counter++]++;

node[i].num.push_back(prev);

}

//node[i].freq[tmp]++;

}

node[i].cnt=counter;

}

return 0;

}

int main()

{

string str;

double p = sqrt(33000)+4;

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

{

if(prime[i]==0)

{

for(int j=i+i;j<33000;j+=i)

prime[j]=1;

}

v.clear();

v.push_back(2);

for(int j=3;j<33000;j++)

{

if(prime[j]==0 && j%2!=0)

v.push_back(j);

}

factorize();

int n,numb;

int a,b;

while(1)

{

getline(cin,str);

if(str=="0")

break;

istringstream s(str);

int c=0;

numb=1;

while(s>>n)

{

if(c==0)

{

a=n;

c=1;

}

else if(c)

{

b=n;

c=0;

numb*=_pow(a,b);

}

NODE tNode = node[numb-1];

//cout<<tNode.num.size()<<"\n";

//cout<<tNode.num[5]<<" "<<tNode.freq[5]<<"\n";

//for(int i=node[numb-1].num.size()-1;i>=0;i++)

for(int i=(tNode.num.size()-1);i>=0;i--)

{

cout<<tNode.num[i]<<" ";//cout<<ii->first<<" "<<ii->second<<" ";

if(i)

cout<<tNode.freq[i]<<" ";

else

cout<<tNode.freq[i]<<"\n";

}

return 0;

}

884

Asif NaeemNovember 7, 2014

#include <iostream>
#include <vector>
#include <math.h>
#include <fstream>
#include <cstdlib>

#define SIZE 1000005

using namespace std;

int arr[1000005];
int prime[1000005];
vector<int> v;



int main()
{

	int n;

	/*prime[2]=0;
	arr[2]=0;
	for(int i=3;i<SIZE;i++)
	{
		arr[i]=0;
		if(i%2==0)
			prime[i]=1;
		else
		prime[i]=0;

	}
	*/
	double p=sqrt(SIZE);
	for(int i=3;i<(p+5);i+=2)
	{
		if(prime[i]==0)
		{
			for(int j=i+i;j<SIZE;j+=i)
			{
				prime[j]=1;
			}
		}
	}

	v.push_back(2);//
	for(int i=3;i<1010;i++)
	{
        if(prime[i]==0 && i%2!=0)
		{
			v.push_back(i);
		}
	}

	//cout<<v.size();

	arr[1]=0;
	arr[2]=1;
		for(int i=3;i<SIZE;i++)
		{
			if(prime[i]==0 && i%2!=0)
			{
				arr[i]+=(arr[i-1]+1);
				continue;
			}
			int tmp = i;

			int j=0;
			while(tmp>=(v[j]*v[j]))
			{
				if(tmp%v[j]==0)
				{
					tmp/=v[j];
					arr[i]++;
					j=-1;
				}
				j++;
			}
			if(tmp)
			arr[i]++;

			arr[i]+=arr[i-1];
		}

		while(cin>>n)
		{
			int sum=0;
			cout<<arr[n]<<"\n";
		}

	return 0;
}

#include <iostream>

#include <vector>

#include <math.h>

#include <fstream>

#include <cstdlib>

#define SIZE 1000005

using namespace std;

int arr[1000005];

int prime[1000005];

vector<int> v;

int main()

{

int n;

/*prime[2]=0;

arr[2]=0;

for(int i=3;i<SIZE;i++)

{

arr[i]=0;

if(i%2==0)

prime[i]=1;

else

prime[i]=0;

}

double p=sqrt(SIZE);

for(int i=3;i<(p+5);i+=2)

{

if(prime[i]==0)

{

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

{

prime[j]=1;

}

v.push_back(2);//

for(int i=3;i<1010;i++)

{

if(prime[i]==0 && i%2!=0)

{

v.push_back(i);

}

//cout<<v.size();

arr[1]=0;

arr[2]=1;

for(int i=3;i<SIZE;i++)

{

if(prime[i]==0 && i%2!=0)

{

arr[i]+=(arr[i-1]+1);

continue;

}

int tmp = i;

int j=0;

while(tmp>=(v[j]*v[j]))

{

if(tmp%v[j]==0)

{

tmp/=v[j];

arr[i]++;

j=-1;

}

j++;

}

if(tmp)

arr[i]++;

arr[i]+=arr[i-1];

}

while(cin>>n)

{

int sum=0;

cout<<arr[n]<<"\n";

}

return 0;

}

Theory: The key to figuring out this problem was to recognize that you needed to resolve cycles in the data – if you follow an item to the item that’s in its spot, and then the one that’s in the next one’s spot, until you reach the original item again, you’ll have a cycle of

Continue Reading “1016” →

306

Asif NaeemSeptember 20, 2014

#include <iostream>
#include <map>
#include <vector>
#include <string>
#include <stdio.h>

/*

10
4 5 3 7 2 8 1 6 10 9
1 Hello Bob
1995 CERC
0
0

Sample Output

BolHeol  b
C RCE

 */
using namespace std;

int arr[202];
vector<char> c_arr[202];
char s[202];


int cycle(int pos)
{
	int org=pos;
	int init=arr[pos];
	int cnt=1;
	c_arr[pos-1].clear();
	c_arr[org-1].push_back(s[arr[pos]]);

	pos=arr[pos];

	while(init!=arr[pos])
	{
		c_arr[org-1].push_back(s[arr[pos]]);
		pos=arr[pos];
		cnt++;
	}

	return cnt;
}

int main()
{
	int n,k,len;
	string str;
	int pos_of_cycle;

	while(cin>>n)
	{
		if(n==0)
		break;
		for(int i=1;i<=n;i++)
		{
			cin>>arr[i];
		}
		while(cin>>k)
		{
			getchar();
			if(k==0)
			break;

			getline(cin,str);

			for(int i=0;i<str.size();i++)
			{
				s[i+1]=str[i];
			}
			for(int i=(str.size()+1);i<=n;i++)
				s[i]=' ';
			for(int pos=1;pos<=n;pos++)
			{
				len = cycle(pos);
				pos_of_cycle=len-1-(k%len);
				cout<<c_arr[pos-1][pos_of_cycle];

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

	}

	return 0;
}

#include <iostream>

#include <map>

#include <vector>

#include <string>

#include <stdio.h>

4 5 3 7 2 8 1 6 10 9

1 Hello Bob

1995 CERC

Sample Output

BolHeol b

C RCE

using namespace std;

int arr[202];

vector<char> c_arr[202];

char s[202];

int cycle(int pos)

{

int org=pos;

int init=arr[pos];

int cnt=1;

c_arr[pos-1].clear();

c_arr[org-1].push_back(s[arr[pos]]);

pos=arr[pos];

while(init!=arr[pos])

{

c_arr[org-1].push_back(s[arr[pos]]);

pos=arr[pos];

cnt++;

}

return cnt;

}

int main()

{

int n,k,len;

string str;

int pos_of_cycle;

while(cin>>n)

{

if(n==0)

break;

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

{

cin>>arr[i];

}

while(cin>>k)

{

getchar();

if(k==0)

break;

getline(cin,str);

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

{

s[i+1]=str[i];

}

for(int i=(str.size()+1);i<=n;i++)

s[i]=' ';

for(int pos=1;pos<=n;pos++)

{

len = cycle(pos);

pos_of_cycle=len-1-(k%len);

cout<<c_arr[pos-1][pos_of_cycle];

}

cout<<"\n";

}

cout<<"\n";

}

return 0;

}

12342

Asif NaeemSeptember 20, 2014

#include <iostream>
#include <stdio.h>
#include <math.h>

using namespace std;

double _max(double a,double b)
{
	if(a>b)
	return a;
	else
	return b;
}

int main()
{
	int t,c=1;
	double a,b,cx;
	cin>>t;

	while(t--)
	{
		cin>>a;
		if(a<=180000)
		{
			cout<<"Case "<<c++<<": "<<0<<"\n";
			continue;
		}
		cx=0;
		if((a-1180000)>0)
		{
			cx+=(a-1180000)*.25;
			a-=(a-1180000);
		}
		if((a-880000)>0)
		{
			cx+=(a-880000)*.2;
			a-=(a-880000);
		}
		if((a-480000)>0)
		{
			cx+=(a-480000)*.15;
			//cout<<"dd1 "<<(a-480000)<<"\n";
			a-=(a-480000);
		}
		if((a-180000)>0)
		{

			b=(a-180000)*.1;
			b=_max(b,2000);
			cx+=b;

		}

		cout<<"Case "<<c++<<": ";
		printf("%.0lf\n",ceil(cx));
	}

	return 0;
}

#include <iostream>

#include <stdio.h>

#include <math.h>

using namespace std;

double _max(double a,double b)

{

if(a>b)

return a;

else

return b;

}

int main()

{

int t,c=1;

double a,b,cx;

cin>>t;

while(t--)

{

cin>>a;

if(a<=180000)

{

cout<<"Case "<<c++<<": "<<0<<"\n";

continue;

}

cx=0;

if((a-1180000)>0)

{

cx+=(a-1180000)*.25;

a-=(a-1180000);

}

if((a-880000)>0)

{

cx+=(a-880000)*.2;

a-=(a-880000);

}

if((a-480000)>0)

{

cx+=(a-480000)*.15;

//cout<<"dd1 "<<(a-480000)<<"\n";

a-=(a-480000);

}

if((a-180000)>0)

{

b=(a-180000)*.1;

b=_max(b,2000);

cx+=b;

}

cout<<"Case "<<c++<<": ";

printf("%.0lf\n",ceil(cx));

}

return 0;

}

355

Asif NaeemSeptember 18, 2014

#include <string>
#include <stdio.h>
#include <sstream>
#include <iostream>

using namespace std;

int fBase,tBase;
string str,str1;
char ch[200];
int k;

int convert()
{
    unsigned long long d;
    unsigned long long r=0;
    unsigned long long _pow=1;
    if(str[str.size()-1]>'9')
    {
        d=str[str.size()-1]-55;
        if(d>=fBase)
        return -1;
    }
    else
    {
    	d=str[str.size()-1]-'0';
    	if(d>=fBase)
        return -1;
    }

    //cout<<_pow<<" "<<d<<"\n";
    r+=d;
    for(int i=str.size()-2;i>=0;i--)
    {
        _pow*=fBase;

        if(str[i]>'9')
        {
            d=str[i]-55;
            if(d>=fBase)
	        return -1;
        }
        else
        {
        	d=str[i]-'0';
        	if(d>=fBase)
	        return -1;
        }
        //cout<<_pow<<" "<<d<<"\n";
        r+=(d*_pow);
    }
    //cout<<"r = "<<r<<"\n";
    k=0;
    if(r==0)
    {
    	ch[k]='0';
    	k++;
    }
    while(r)
    {
        if((r%tBase)>9)
            ch[k]=(((r%tBase)+55)+'\0');
        else
            ch[k]=((r%tBase)+'0');
        r/=tBase;
        k++;
    }


    return 0;
}

int main()
{
    while(cin>>fBase)
    {

        cin>>tBase;
        cin>>str;
        str1="";
        //cout<<str<<"\n";
        if(convert()==-1)
        cout<<str<<" is an illegal base "<<fBase<<" number\n";
        else
        {
        	cout<<str<<" base "<<fBase<<" = ";
        	for(int i=k-1;i>=0;i--)
            printf("%c",ch[i]);
            cout<<" base "<<tBase<<"\n";

        }
    }

    return 0;
}

#include <string>

#include <stdio.h>

#include <sstream>

#include <iostream>

using namespace std;

int fBase,tBase;

string str,str1;

char ch[200];

int k;

int convert()

{

unsigned long long d;

unsigned long long r=0;

unsigned long long _pow=1;

if(str[str.size()-1]>'9')

{

d=str[str.size()-1]-55;

if(d>=fBase)

return -1;

}

else

{

d=str[str.size()-1]-'0';

if(d>=fBase)

return -1;

}

//cout<<_pow<<" "<<d<<"\n";

r+=d;

for(int i=str.size()-2;i>=0;i--)

{

_pow*=fBase;

if(str[i]>'9')

{

d=str[i]-55;

if(d>=fBase)

return -1;

}

else

{

d=str[i]-'0';

if(d>=fBase)

return -1;

}

//cout<<_pow<<" "<<d<<"\n";

r+=(d*_pow);

}

//cout<<"r = "<<r<<"\n";

k=0;

if(r==0)

{

ch[k]='0';

k++;

}

while(r)

{

if((r%tBase)>9)

ch[k]=(((r%tBase)+55)+'\0');

else

ch[k]=((r%tBase)+'0');

r/=tBase;

k++;

}

return 0;

}

int main()

{

while(cin>>fBase)

{

cin>>tBase;

cin>>str;

str1="";

//cout<<str<<"\n";

if(convert()==-1)

cout<<str<<" is an illegal base "<<fBase<<" number\n";

else

{

cout<<str<<" base "<<fBase<<" = ";

for(int i=k-1;i>=0;i--)

printf("%c",ch[i]);

cout<<" base "<<tBase<<"\n";

}

return 0;

}

389

Asif NaeemSeptember 10, 2014

#include <iostream>
#include <string>
#include <stdio.h>
#include <sstream>

using namespace std;

int fBase,tBase;
string str,str1;
char ch[7];

int convert()
{
	unsigned long long d;
	int k=7;
	unsigned long long r=0;
	unsigned long long _pow=1;
	if(str[str.size()-1]>'9')
	{
		d=str[str.size()-1]-55;
	}
	else
		d=str[str.size()-1]-'0';
	//cout<<_pow<<" "<<d<<"\n";
	r+=d;
	for(int i=str.size()-2;i>=0;i--)
	{
		_pow*=fBase;

		if(str[i]>'9')
		{
			d=str[i]-55;
		}
		else
			d=str[i]-'0';
		//cout<<_pow<<" "<<d<<"\n";
		r+=(d*_pow);
	}
	//cout<<"r = "<<r<<"\n";
	k=7;
	if(r==0)
	{
		k--;
		ch[k]='0';
	}
	while(r)
	{
		k--;
		if((r%tBase)>9)
			ch[k]=(((r%tBase)+55)+'\0');
		else
			ch[k]=((r%tBase)+'0');
		r/=tBase;
		if(k==0)
		{
			if(r)
			return -1;
			else
			break;
		}
	}

	for(int i=k-1;i>=0;i--)
	ch[i]=' ';

	return 0;
}

int main()
{
	while(cin>>str)
	{
		cin>>fBase>>tBase;
		str1="";
		//cout<<str<<"\n";
		if(convert()==-1)
		cout<<"  ERROR\n";
		else
		{
			printf("%s\n",ch);

		}
	}

	return 0;
}

#include <iostream>

#include <string>

#include <stdio.h>

#include <sstream>

using namespace std;

int fBase,tBase;

string str,str1;

char ch[7];

int convert()

{

unsigned long long d;

int k=7;

unsigned long long r=0;

unsigned long long _pow=1;

if(str[str.size()-1]>'9')

{

d=str[str.size()-1]-55;

}

else

d=str[str.size()-1]-'0';

//cout<<_pow<<" "<<d<<"\n";

r+=d;

for(int i=str.size()-2;i>=0;i--)

{

_pow*=fBase;

if(str[i]>'9')

{

d=str[i]-55;

}

else

d=str[i]-'0';

//cout<<_pow<<" "<<d<<"\n";

r+=(d*_pow);

}

//cout<<"r = "<<r<<"\n";

k=7;

if(r==0)

{

k--;

ch[k]='0';

}

while(r)

{

k--;

if((r%tBase)>9)

ch[k]=(((r%tBase)+55)+'\0');

else

ch[k]=((r%tBase)+'0');

r/=tBase;

if(k==0)

{

if(r)

return -1;

else

break;

}

for(int i=k-1;i>=0;i--)

ch[i]=' ';

return 0;

}

int main()

{

while(cin>>str)

{

cin>>fBase>>tBase;

str1="";

//cout<<str<<"\n";

if(convert()==-1)

cout<<" ERROR\n";

else

{

printf("%s\n",ch);

}

return 0;

}

12712

Asif NaeemSeptember 1, 2014

#include <iostream>

using namespace std;

int main()
{
	int t,c=0;
	int MX;
	int L,M,N;
	unsigned long long sum,tmp;

	cin>>t;

	while(t--)
	{
		cin>>L>>M>>N;
		c++;
		MX=L*L;
		tmp=1;
		for(int i=M-1;i>=0;i--)
		{
			tmp=tmp*(MX-i);
			tmp%=10000000000007;
		}

		sum=0;

		for(int j=1;j<=N-M+1;j++)
		{
			sum+=tmp;
			sum%=10000000000007;
			tmp*=(MX-M+1-j);
			tmp%=10000000000007;
		}

		cout<<"Case "<<c<<": ";
		cout<<sum<<"\n";
	}

	return 0;
}

#include <iostream>

using namespace std;

int main()

{

int t,c=0;

int MX;

int L,M,N;

unsigned long long sum,tmp;

cin>>t;

while(t--)

{

cin>>L>>M>>N;

c++;

MX=L*L;

tmp=1;

for(int i=M-1;i>=0;i--)

{

tmp=tmp*(MX-i);

tmp%=10000000000007;

}

sum=0;

for(int j=1;j<=N-M+1;j++)

{

sum+=tmp;

sum%=10000000000007;

tmp*=(MX-M+1-j);

tmp%=10000000000007;

}

cout<<"Case "<<c<<": ";

cout<<sum<<"\n";

}

return 0;

}

12716

Asif NaeemAugust 31, 2014

#include <iostream>
using namespace std;

int a[30000005];
int main() {

   int t,n,c=0;
   for(int i=1;i<30000005;i++)
   {
      for(int j=i<<1;i+j<30000005;j+=i)
      {
        if(((i+j)&j)==j)
        a[i+j]++;
      }
   }

   for(int i=1;i<30000005;i++)
   a[i]+=a[i-1];
   cin>>t;

   while(t--)
   {
      cin>>n;
      c++;
      cout<<"Case "<<c<<": "<<a[n]<<"\n";
   }

   return 0;
}

#include <iostream>

using namespace std;

int a[30000005];

int main() {

int t,n,c=0;

for(int i=1;i<30000005;i++)

{

for(int j=i<<1;i+j<30000005;j+=i)

{

if(((i+j)&j)==j)

a[i+j]++;

}

for(int i=1;i<30000005;i++)

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

cin>>t;

while(t--)

{

cin>>n;

c++;

cout<<"Case "<<c<<": "<<a[n]<<"\n";

}

return 0;

}

10104

Asif NaeemAugust 31, 2014

//Extended euclid Algorithm
#include <iostream>

using namespace std;

long long int gcd(long long int a, long long int b)
{
     if(b==0)
     return a;
     else
     return gcd(b,a%b);
}

int main()
{
    long long int a,b,g,q,temp,t1,t2;


    while(cin>>a>>b)
    {
       //g=gcd(a,b);
       long long int prevx=1,x=0,y=1,prevy=0;

       while(b)
       {
         q=a/b;
         t1=x;
         x=prevx-q*x;
         prevx=t1;
         t2=y;
         y=prevy-q*y;
         prevy=t2;
         temp=a;
         a=b;
         b=temp%b;
       }
       cout<<prevx<<" "<<prevy<<" "<<a<<"\n";
    }
    return 0;
}

//Extended euclid Algorithm

#include <iostream>

using namespace std;

long long int gcd(long long int a, long long int b)

{

if(b==0)

return a;

else

return gcd(b,a%b);

}

int main()

{

long long int a,b,g,q,temp,t1,t2;

while(cin>>a>>b)

{

//g=gcd(a,b);

long long int prevx=1,x=0,y=1,prevy=0;

while(b)

{

q=a/b;

t1=x;

x=prevx-q*x;

prevx=t1;

t2=y;

y=prevy-q*y;

prevy=t2;

temp=a;

a=b;

b=temp%b;

}

cout<<prevx<<" "<<prevy<<" "<<a<<"\n";

}

return 0;

}

Theory: The pseudo code of the extended euclid algorithm: xgcd(a,b): prevx, x = 1, 0; prevy, y = 0, 1 while (b!=0) { q = a/b x = prevx – q*x; prevx= x; y = prevy – q*y; prevy= y; a = b; b= a % b; } return a, prevx, prevy [button color=”red”

Continue Reading “10104” →

Category: Number Theory

516

884

1016

306

12342

355

389

12712

12716

10104

Archives

Categories