java语言实现：数论经典问题 除法表达 ,无平方因子数 ，直线上的点，同余与模算术 大整数取模 幂取模，模线性方程

 

package com.supermars.practice;

import java.util.Scanner;

public class 除法表达式 {
	static Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		while (cin.hasNext()) {
			String s = cin.next();
			String X[] = s.split("/");
			int fenmu = 0;
			loop: for (int i = 0; i < X.length; i++) {
				fenmu = Integer.parseInt(X[i]);
				for (int j = 0; j < i; j++) {
					int g = gcd(Integer.parseInt(X[j]), fenmu);
					fenmu /= g;
					if (fenmu == 1)
						break loop;
				}
				for (int j = i + 1; j < X.length; j++) {
					int g = gcd(Integer.parseInt(X[j]), fenmu);
					fenmu /= g;
					if (fenmu == 1)
						break loop;
				}

			}

			System.out.println((fenmu == 1) ? "YES" : "NO");

		}
	}

	private static int gcd(int a, int b) {

		return b == 0 ? a : gcd(b, a % b);
	}
}

package com.supermars.practice;

import java.util.Arrays;
import java.util.Scanner;

public class 无平方因子数 {
	static Scanner cin = new Scanner(System.in);
	static int vis[] = new int[1<<10];
	static 	int prim[];

	public static void main(String[] args) {
		while (cin.hasNext()) {
			int n = cin.nextInt();
			int m = cin.nextInt();
			//int t = (int) Math.sqrt(m + 0.5);
			
			prim = new int[m];
			
			int cnt = 0;
			for (int i = 2; i <= m; i++) {
				if (vis[i] == 0)
					prim[cnt++] = i;
				for (int j = i * i; j <= m; j += i) {
					vis[j] = 1;

				}
			}
			
			
			System.out.println(cnt);
/*
			int count=cnt;
			for (int i = 0; i < cnt; i++) {
				int p = prim[i]*prim[i];
				if (p < prim[cnt - 1]) {
					int index = Arrays.binarySearch(prim, p);
					System.out.print(index+" ");
					if (index>=0){
						prim[index] = Integer.MAX_VALUE;
						count--;
					}				
				}
			}*/
			

		}
	}
}

package com.supermars.practice;

import java.util.Scanner;

public class 直线上的点 {
	static Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		// ax+by=c;
		while (cin.hasNext()) {
			int a = cin.nextInt();
			int b = cin.nextInt();
			int c = cin.nextInt();

			int X1 = cin.nextInt();// [X1,X2]
			int X2 = cin.nextInt();// [Y1,Y2]
			int Y1 = cin.nextInt();
			int Y2 = cin.nextInt();
			int g = gcd(a, b);
			if (c % g != 0) {// g|c --->Xnew=c%g*X0 (k*X0,k=c%g,c%g==Int)
				System.out.println("NO");
				continue;
			}
			int m = c % g, k = 1;
			if (m == 0) {
				k = c / g;

				for (int x = X1; x <= X2; x++) {
					double y = (c - a * x) / b;
					int yy = (int) y;
					if (y == yy && yy * k >= Y1 && yy * k <= Y2 && x * k >= X1
							&& x * k <= X2) {
						System.out.print(x * k + " " + yy * k + "\n");
					}
				}

			}
		}

	}

	private static int gcd(int a, int b) {
		return (b == 0) ? a : gcd(b, a % b);
	}

}

package com.supermars.practice;

import java.util.Scanner;

/**
123456789*987654321
123456789+987654321
123456789-987654321
 * @author supermars
 *
 */
public class 同余与模算术 {
	static Scanner cin = new Scanner(System.in);
	public static void main(String[] args) {
		while (cin.hasNext()) {
			String s = cin.next();
			String[] sa;
			String op = "*";
			sa = s.split("\\*");
			if (sa.length == 1) {
				sa = s.split("\\+");
				op = "+";
				if (sa.length == 1) {
					sa = s.split("\\-");
					op = "-";
				}
			}

			long a = Long.parseLong(sa[0]);
			long b = Long.parseLong(sa[1]);

			long ret = 0, n = 10;
			if (op == "*") {
				ret = mul_mod(a, b, n);
			}
			if (op == "+") {
				ret = add_mod(a, b, n);
			}
			if (op == "-") {
				ret = sub_mod(a, b, n);
			}
			System.out.println(ret);

		}

	}

	private static long sub_mod(long a, long b, long n) {
		a %= n;
		b %= n;
		return (a - b + n) % n;
	}

	private static long add_mod(long a, long b, long n) {
		return ((a %= n) + (b %= n)) % n;
	}

	private static long mul_mod(long a, long b, long n) {
		a %= n;
		b %= n;
		return a * b % n;
	}
}

package com.supermars.practice;

import java.util.Scanner;

public class 大整数取模 {
	static Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		while (cin.hasNext()) {
			String n = cin.next();
			int m = cin.nextInt();

			int ans = 0;
			for (int i = 0; i < n.length(); i++) {
				int t = ((int) n.charAt(i));
				ans = (ans * 10 + t) % m;
			}
			System.out.println(ans);
		}
	}
}

package com.supermars.practice;

import java.util.Scanner;

public class 幂取模 {
	static Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		while (cin.hasNext()) {
			int a = cin.nextInt(); // a,n,m<=10^9
			int n = cin.nextInt();
			int m = cin.nextInt();
			long ans = 1;
			for (int i = 1; i <= n; i++) {
				ans *= a % m;
				ans %= m;
			}
			// ab mode n =(a mode n)(b mode n)mode n
			System.out.println(ans % m);

		}

	}
}

package com.supermars.practice;

import java.util.Scanner;

public class 模线性方程 {
	static Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		while (cin.hasNext()) {
			int a = cin.nextInt();
			int b = cin.nextInt();
			int n = cin.nextInt();

			int g = gcd(a, n);
			int k = (g % b == 0) ? g / b : 0;
			if (k == 0)
				System.out.println("No");
			// 求解 ax-ny=b上的点
			

		}
	}

	private static int gcd(int a, int b) {
		return (b == 0) ? a : gcd(b, a % b);
	}

}