/*
A Pythagorean triple is a set of three positive integers (a, b, c)
that satisfy the equation:
a^2 + b^2 = c^2
These represent the side lengths of a right‑angled triangle.
A *primitive* Pythagorean triple is one in which:
- gcd(a, b, c) = 1 (no common divisor greater than 1)
- a, b, and c are positive integers
- a < b < c
Examples of primitive triples include:
(3, 4, 5)
(5, 12, 13)
(8, 15, 17)
*/
#include <iostream>
#include <cmath>
// Compute gcd of two integers
int gcd(int a, int b) {
while (b != 0) {
int t = b;
b = a % b;
a = t;
}
return a;
}
// Check if (a, b, c) is a primitive Pythagorean triple
bool isPrimitiveTriple(int a, int b, int c) {
if (a*a + b*b != c*c)
return false;
return gcd(a, b) == 1 && gcd(b, c) == 1 && gcd(a, c) == 1;
}
// Find and print the first 3 primitive Pythagorean triples
void findFirstThreePrimitiveTriples() {
int count = 0;
for (int a = 1; a < 200; a++) {
for (int b = a + 1; b < 200; b++) {
int c = sqrt(a*a + b*b);
if (c*c == a*a + b*b) {
if (isPrimitiveTriple(a, b, c)) {
std::cout << "(" << a << ", " << b << ", " << c << ")" << std::endl;
count++;
if (count == 3)
return;
}
}
}
}
}
int main() {
std::cout << "First 3 primitive Pythagorean triples:" << std::endl;
findFirstThreePrimitiveTriples();
}
/*
run:
First 3 primitive Pythagorean triples:
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
*/
