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Problem45.java
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Problem45.java
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/*
* Prompt: Find the next triangle number [after 40755] that is also pentagonal and hexagonal.
*
* Execute: javac Problem45.java; java Problem45; rm Problem45.class
*
* Answer: 1533776805
*/
public class Problem45 {
public static void main(String[] args) {
for (int i = 2; ; i++) {
long t = triangular(i);
if (pentagonal_inverse(t) != 0 && t != 40755) { // 40755 is given in prompt, hardcoded to ignore
if (hexagonal_inverse(t) != 0) {
System.out.println(t);
System.exit(0);
}
}
}
}
public static long triangular(long n) {
return n * (n + 1) / 2;
}
// Finds x such that x(3x-1)/2 = given n
// Uses inverse of pentagonal function:
// (1 + sqrt(1+24x)) / 6
// Returns x if exists, otherwise 0
public static int pentagonal_inverse(long n) {
double a = Math.sqrt(24 * n + 1);
if (a == Math.floor(a)) {
double b = (a + 1) / 6;
if (b == Math.floor(b)) {
return (int) b;
}
}
return 0;
}
// Finds x such that x(2x-1) = given n
// Uses inverse of hexagonal function:
// (1 + sqrt(1+8x)) / 4
// Returns x if exists, otherwise 0
public static int hexagonal_inverse(long n) {
double a = Math.sqrt(8 * n + 1);
if (a == Math.floor(a)) {
double b = (a + 1) / 4;
if (b == Math.floor(b)) {
return (int) b;
}
}
return 0;
}
}