Cardano Triplets
June 20, 2009
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.
Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter