My favorite number – 1729

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:

http://en.wikipedia.org/wiki/1729_(number)

 

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One Response to My favorite number – 1729

  1. Amitabha Tripathi says:

    Hi, Alok. Just stumbled upon your puzzle site while looking for something else. I only wish to point out two things about the “taxicab” number, as 1729 is now popularly called. First, the name associated with it is Srinivasa RAMANUJAN (ending in “n”). Second, the incident is a fact accorded to many sources (including “A Man Who Knew Infinity” by Robert Kanigel). The story is that G.H. Hardy was visiting Ramanujan as he was recovering in a nursing home in Putney, England. The rest is good.

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