For those of you who are number buffs, I am assuming you know this already, but if not, I thought you might enjoy this. This was told to my brother and I as a story when my father told us about Ramanujam, and since then I have always been trying to get this number as either a car license plate or as a telephone number, though have succeeded only once so far.
The story goes like this (though I am not sure if this is 100% true) – Hardy (Ramanujam’s British colleague) came to meet Ramanujam in the hospital and told him that he bought a new car. Hardy told Ramanujam that the number of the car is 1729, when Ramanujam inquired. Ramanujam immediately told Hardy that it is a very special number. When asked why, he said that 1729 is the smallest number that can be expressed as a sum of cubes of two different positive integers in two different ways:
1x1x1 + 12x12x12 = 1729
10x10x10 + 9x9x9 = 1729
When I looked up 1729 last year on Wikipedia, I found to my surprise and excitement that if we twist the problem to not limit it to positive integers, 91 is the smallest such number – figure out how? For a more detailed version of this, look at: