id	title	challengeType	forumTopicId	dashedName
5900f4671000cf542c50ff7a	Problem 251: Cardano Triplets	5	301899	problem-251-cardano-triplets

--description--

A triplet of positive integers (a,b,c) is called a Cardano Triplet if it satisfies the condition:

\sqrt[3]{a + b \sqrt{c}} + \sqrt[3]{a - b \sqrt{c}} = 1

For example, (2,1,5) is a Cardano Triplet.

There exist 149 Cardano Triplets for which a + b + c ≤ 1000.

Find how many Cardano Triplets exist such that a + b + c ≤ 110\\,000\\,000.

--hints--

cardanoTriplets() should return 18946051.

assert.strictEqual(cardanoTriplets(), 18946051);

function cardanoTriplets() {

  return true;
}

cardanoTriplets();

// solution required