## Problem:

The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 23 [×] 32 [×] 7, so rad(504) = 2 [×] 3 [×] 7 = 42.

We shall define the triplet of positive integers (a, b, c) to be an abc-hit if:

1. GCD(a, b) = GCD(a, c) = GCD(b, c) = 1
2. a [<] b
3. a + b = c
4. rad(abc) [<] c

For example, (5, 27, 32) is an abc-hit, because:

1. GCD(5, 27) = GCD(5, 32) = GCD(27, 32) = 1
2. 5 [<] 27
3. 5 + 27 = 32
4. rad(4320) = 30 [<] 32

It turns out that abc-hits are quite rare and there are only thirty-one abc-hits for c [<] 1000, with [∑]c = 12523.

Find [∑]c for c [<] 120000.

-59231

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 27 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p027 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p027().run());	}			public String run() {		int bestNum = 0;		int bestA = 0;		int bestB = 0;		for (int a = -1000; a <= 1000; a++) {			for (int b = -1000; b <= 1000; b++) {				int num = numberOfConsecutivePrimesGenerated(a, b);				if (num > bestNum) {					bestNum = num;					bestA = a;					bestB = b;				}			}		}		return Integer.toString(bestA * bestB);	}			private static int numberOfConsecutivePrimesGenerated(int a, int b) {		for (int i = 0; ; i++) {			int n = i * i + i * a + b;			if (n < 0 || !Library.isPrime(n))				return i;		}	}	}

## Follow Me

If you like our content, feel free to follow me to stay updated.

## Subscribe

Enter your email address:

We hate spam as much as you do.

## Upload Material

Got an exam, project, tutorial video, exercise, solutions, unsolved problem, question, solution manual? We are open to any coding material. Why not upload?
Copyright © 2012 - 2014 Java Problems  --  About  --  Attribution  --  Privacy Policy  --  Terms of Use  --  Contact