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Problem 251

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Cardano Triplets

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

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.

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卡尔达诺三元组

若正整数三元组(a,b,c)满足如下性质，就被称为卡尔达诺三元组：

例如，(2,1,5)就是一个卡尔达诺三元组。

存在149个卡尔达诺三元组满足a+b+c ≤ 1000。

存在多少个卡尔达诺三元组a+b+c ≤ 110,000,000？

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