1.2 KiB
1.2 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4461000cf542c50ff59 | Problem 218: Perfect right-angled triangles | 5 | 301860 | problem-218-perfect-right-angled-triangles |
--description--
Consider the right-angled triangle with sides a=7, b=24 and c=25.
The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.
Moreover it is a primitive right-angled triangle as gcd(a,b) = 1 and gcd(b,c) = 1.
Also c is a perfect square.
We will call a right-angled triangle perfect if:
- it is a primitive right-angled triangle
- its hypotenuse is a perfect square
We will call a right-angled triangle super-perfect if:
- it is a perfect right-angled triangle
- its area is a multiple of the perfect numbers 6 and 28.
How many perfect right-angled triangles with c ≤ {10}^{16} exist that are not super-perfect?
--hints--
perfectRightAngledTriangles() should return 0.
assert.strictEqual(perfectRightAngledTriangles(), 0);
--seed--
--seed-contents--
function perfectRightAngledTriangles() {
return true;
}
perfectRightAngledTriangles();
--solutions--
// solution required