The smallest number that can be written as a sum of two cubes of integers in two (non-trivially) different ways is 91, not 1729. 91 = 3^3 + 4^3 = 6^3 + (-5)^3. I wonder if Ramanujan specified to Hardy that he was specifically referring to the natural numbers, because the folklore never seems to specify that.

The smallest number that can be written as a sum of two cubes of integers in two (non-trivially) different ways is 91, not 1729. 91 = 3^3 + 4^3 = 6^3 + (-5)^3. I wonder if Ramanujan specified to Hardy that he was specifically referring to the natural numbers, because the folklore never seems to specify that.