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Friday, July 17, 2009

1729 - TAXICAB NUMBER

1729 is smallest taxicab number , i.e., the smallest number representable in two ways as a sum of cubes. It is given by

1729 = 12³ + 1³

1729 = 10³ + 9³

The number derives its name from the following story:

G. H. Hardy told about Ramanujan. I remember once going to see him when he was ill . I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."



1729 is the second taxicab number (the first is 2= 1^3 + 1^3). The number was also found in one of Ramanujan's notebooks dated years before the incident.




"Every positive integer is one of Ramanujan's personal friends."—J.E. Littlewood, on hearing of the taxicab incident


More details are available on the attached link.
Source(s):
http://en.wikipedia.org/wiki/1729_(number)




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