Chapter 2: 4-digit Kaplan number, search even digit Kaplan number, search n-digit 2-segment sum square number, m-digit ingenious square number without 0, specify the number to form a 7-digit square nu

//4 Bit Caprica number  
int main()
{
    
	int a, b, c, x, y;
	printf(" 4 The number of bit Caprica is ：");
	c = (int)sqrt(1000);
	for (b = c + 1; b <= 99; b++) //  enumeration 2 digit b
	{
    
		a = b * b;
		x = a / 100;  // a  It is divided into two parts 2 Male 
		y = a % 100; //  Segment and condition inspection  
		if( y >= 10 && b == (x + y))
		printf("%d, ", a);
	}
	
	return 0;
}

result ：

// Search the even digit number of Caprica  
int main()
{
    
	double a, b, m, w, x, y; 
	int k, n; long c, d;
	printf(" Please enter an even number n(n≤14) :");
	scanf("%d", &n); 
	if (n % 2 > 0)
	{
    
		printf("  Please enter an even number !\n");
			return 0;
	}
	printf(" % d The number of bit Caprica is ： \n", n);
	for (m = 1, k = 2;k <= n; k++)m *= 10;
	for (w = 1, k = 1 ; k <= n / 2; k++)w *= 10;
			c = (long)pow(m, 0.5);
			d = (long)pow(10 * m - 1, 0.5); //  Find the starting point and ending point of the loop on enumeration  
			for (b = c + 1; b <= d; b++)
			{
    
				a = b * b;
					x = floor(a / w);
					y = fmod(a, w);//n Bit square a Divided into front and back numbers x、y
					if (b == x + y && y >= w / 10) // Segment and condition inspection 
						printf(" %.0f= (%.0f+%.0f)^2 \n",a,x,y);
			}
	return 0;
}

result ：

// Search for n position 2 Segment sum square 
int main()
{
    
	double a, b, m, w, x, y; 
	long c, d; int k, n, s = 0;
	printf("  Please enter a positive integer n (3<n<16:");
	scanf(" %d", &n);
	for (m = 1, k = 2; k <= n; k++) m *= 10;
	c = (long)pow(m, 0.5);
	d = (long)pow(10 * m - 1, 0.5);
	for (b = c + 1; b <= d; b++)
	{
    
		a = b * b;
		w = 1;
		for (k = 1; k <= n - 1; k++)
		{
    
			w *= 10;
			x = floor(a / w);
			y = fmod(a, w);
			if (b == x + y && y > 0)
			{
    
				s++;
				printf(" % .0f = （ % .0f + % .0f） ^ 2\n", a, x, y);
			}
		}
	}


	if (s > 0)
		printf(" common %d individual %d  position 2 Segment sum square  \n", s, n);
	else printf(" No,  % d position 2 Segment sum square . \n", n) ; 
}

result ：

//m Bit does not contain 0 Clever square of 
int main()
{
    
	int k, m, n, i, x, b[10];
	long t, t1, t2, y, d, f;
	printf("  hold  1,2,..,9 this 9 Choose a number m individual , ");
	printf("  Combine into squares without repeating numbers .\n");
	printf("  Please enter the number of square digits m:");
	scanf("%d", &m);
	n = 0;
	t = 1;
	for (y = 1; y <= m - 1; y++)
		t = t * 10;
	t1 = (long)sqrt(t);
	t2 = (long)sqrt(10 * t);
	for (y = t1 + 1; y <= t2; y++)
	{
    
		f = y * y;
		d = f;
		for (i = 1; i <= 9; i++)
			b[i] = 0;
		for (x = 0, i = 1; i <= m; i++)
		{
    
			k = f % 10;
			f = f / 10;
			if (k == 0 || (++b[k] > 1))
			{
    
				x = 1;
				break;
			}
		}
		if (x == 0)
		{
    
			n++;
			printf(" %1d=%d^2", d, y);
			if (n % 3 == 0) printf("\n");
		}
	}
	printf(" \n  common %d individual \n", n);
	return 0;
}

result ：

int main()
{
    
	int k, m, n, t, f[10]; 
	long a, b, c, d, w; 
	printf("  Numbers 2、3、5、6、7、8、9 The square of the total permutation of ：\n");
	n = 0;
	b = (long)sqrt(2356789);
	c = (long)sqrt(9876532);
	for (a = b; a <= c; a++)
	{
    
		d = a * a; w = d; // Make sure d Is the square number 
		for (k = 0; k <= 9; k++) f[k] = 0;
		while (w > 0)
		{
    
			m = w % 10;
			f[m]++;
			w = w / 10;
		}
		for (t = 0, k = 1; k <= 9; k++)
			if (f[k] > 1) t = 1; // Test whether the three square numbers have duplicate numbers  
		if (t == 0 && f[0] + f[1] + f[4] == 0) // There is no number in the test square 0、1、4 
		{
    
			n++;
			printf(" %2d:", n);
			printf(" %1d=%1d 2 \n", d, a);
		}
	}
	printf("  A total of more than %d individual ", n);
	return 0;
}

result ：

// Find the Pythagorean array in the specified interval 
int main()
{
    
	int a, b, n;
	long x, y, z, d;
	printf("  Please enter the interval [a,6] The upper and lower a,b: "); 
	scanf("%d, %d", &a, &b);
	printf("  Section [%d,%d] The Pythagorean array in has ：\n",a,b);
	n=0;
	for (x=a;x<=b-2;x++)
		for (y = x + 1; y <= b - 1; y++)
		{
    
			d = x * x + y * y;
			z = sqrt(d); //2 by x, The sum of squares of  
			if (z > b) break;
			if (z * z == d) // Output when the conditions for the number of hook shares are met  
			{
    
				n++;
				printf(" %ld^2+%ld^2=%1d^2 \n", x, y, z);
			}
		}
	printf("  common %d  Number of shares in the group ", n);
	return 0;
}

result ：

//, Find the inverted Pythagorean array in the specified interval 
int main()
{
    
	int a, b, n;
	long x, y, z;
	printf("  Please enter the interval [a,6] The upper and lower a,b: "); 
	scanf("%d,%d", &a, &b);
	printf("  Section [%d,%d] The Pythagorean array in has ：\n",a,b);
	n=0;
	for(z = a; z <= b -2; z++)
	for(y = z + 1;y <=b - 1; y++)
	for(x = y + 1;x <= b;x++)
		
		
			if(z*z*( x * x + y * y) == x*x*y*y)
			{
    
				n++;
				printf(" 1/%ld^2+1/%ld^2=1/%1d^2 \n", x, y, z);
			}
				
			
		
	printf("  common %d  Group handstand hook number ", n);
	return 0;
}

result ：