47 lines
812 B
Markdown
47 lines
812 B
Markdown
---
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id: 5900f4671000cf542c50ff7a
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title: 'Problem 251: Cardano Triplets'
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challengeType: 5
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forumTopicId: 301899
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dashedName: problem-251-cardano-triplets
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---
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# --description--
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A triplet of positive integers ($a$,$b$,$c$) is called a Cardano Triplet if it satisfies the condition:
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$$\sqrt[3]{a + b \sqrt{c}} + \sqrt[3]{a - b \sqrt{c}} = 1$$
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For example, (2,1,5) is a Cardano Triplet.
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There exist 149 Cardano Triplets for which $a + b + c ≤ 1000$.
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Find how many Cardano Triplets exist such that $a + b + c ≤ 110\\,000\\,000$.
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# --hints--
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`cardanoTriplets()` should return `18946051`.
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```js
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assert.strictEqual(cardanoTriplets(), 18946051);
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```
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# --seed--
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## --seed-contents--
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```js
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function cardanoTriplets() {
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return true;
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}
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cardanoTriplets();
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```
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# --solutions--
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```js
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// solution required
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```
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