Problem 251
20 June 2009
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.