**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.

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.

**Solution:**

648

**Code:**

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

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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