Counting

Lesson 17 of 20 in Coddy's Mathematical Riddles course.

A Pythagorean triplet {a, b, c} forms right angle triangle.

Let p be the perimeter of a right angle triangle with integer length sides, {a, b, c}.

There is exactly one triplet for p=12: {3,4,5}, p=24: {6,8,10} and for p=30: {5,12,13}.

There are exactly three triplets for p = 120: {20,48,52}, {24,45,51}, {30,40,50}.

In contrast, there are no triplet for p=20.

For p≤120, there is one p with three triplets (p=120), three p with two triplets (p=60,84,90), and exactly 13 p with just one triplet.

Challenge

Hard

How many p≤1000 with just one triplet?

Write a function count1PythagoreanTripletSolution that get an integer N, and return the number of integers p≤N that only one integer Pythagorean triplet.

Try it yourself

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include "solution.h"

int main() {
    int n;
    if (scanf("%d", &n) != 1) n = 0;
    int r = count1PythagoreanTripletSolution(n);
    printf("%d\n", r);
    return 0;
}