Cardano triplet
= Cardano triplet
{c}
A triple of <positive integers> $(a,b,c)$ satisfying $\sqrt[3]{a+b\sqrt c}+\sqrt[3]{a-b\sqrt c}=1$, with real cube roots. Cubing the equality yields the equivalent <integer> identity $27b^2c=(a+1)^2(8a-1)$. In particular $a=3k-1$ for a <positive integer> $k$, and the condition becomes $b^2c=k^2(8k-3)$.