Question

Which two pairs of numbers have cubes that add up to 1729? because there are two pairs of numbers to find, you should select a total of four numbers from the list below?

Answer 1

It is called the hardy Ramanujan's number, named after the Indian mathematician, Srinivasa Ramanujan, and British Mathematician G. H Hardy. 
Hardy went to visit Ramanujan while he was ill. He noticed that the number of the taxi he went in was 1729, which he thought was a dull number.

1729 = 12³ + 1³ 
1729 = 10³ + 9³ 

Fujiwara claimed that he proved there are only four numbers that have the property. Even though it seems to be true, he never has shown his proof. No other natural number, other than 1729, can be expressed as a sum of the cubes of two natural numbers in two different ways.