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Ramanujan Number – 1729 (Taxi-Cab problem)

The story of 1729

This article tells the speciality of the number 1729.

1729 is called as Ramanujan number. There is an interesting story behind this number. The explanation of stupendous mathematical concept shows how Ramanujan is zealous about mathematical number theory. Actually a taxi is the reason behind this. Hence the story is also called as “Taxi cab problem”.

Ramanujan Numbers Image

Ramanujan number - 1729


“Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxicab number. Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxicab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’”.


“Taxicab (N)” is defined as the lowest number that can be formed by the sum of two cubes in “N” different ways, Cabtaxi(N) is defined as the lowest number that can be formed by the sum and/or difference of two cubes in “N” different ways. Here, 1729 can be represented as, 13 + 123 = 93 + 103.
1729 is the minimum positive number that can be represented in the above format.

I3 + J3 = K3 + L3.


Ramanujan number theory 1729
Hardy and Ramanujan - Discussion of 1729
Taxi cab(1) problem
Cab taxt number sequences