Cardano Triplet

Learn how to calculate Cardano Triplets.

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Problem

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

a+bc3+abc3=1\sqrt[3]{a+b \sqrt{c}} + \sqrt[3]{a-b \sqrt{c}} = 1

For example, (2,1,5) is a Cardano Triplet. Write a progam to generate all Cardano Triplets that exist, such that (a+b+c)<=100( a + b + c ) <= 100.

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