Permalink Submitted by Anonymous on November 11, 2015

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.

## 1729 must specify natural numbers

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.