## Problem:

Let r be the remainder when (a[−]1)n + (a+1)n is divided by a2.

For example, if a = 7 and n = 3, then r = 42: 63 + 83 = 728 [≡] 42 mod 49. And as n varies, so too will r, but for a = 7 it turns out that rmax = 42.

For 3 [≤] a [≤] 1000, find [∑] rmax.

648

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

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 20 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p020 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p020().run());	}			public String run() {		String temp = Library.factorial(100).toString();		int sum = 0;		for (int i = 0; i < temp.length(); i++)			sum += temp.charAt(i) - '0';		return Integer.toString(sum);	}	}

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