What is special about this number 1729 ─?
Answer: This is
the only known number that is a sum of two cubes n two different ways.
Example: 10ᶾ + 9ᶾ = 1729, 12ᶾ + 1ᶾ = 1729
This is popularly known as Ramanujam’s number. There is an
interesting story about it. The story goes this way. When Ramanujam was sick in
the hospital, Prof. Hardy, his tutor paid him a visit. Prof. Hardy told
Ramanujam that he rode a taxicab to the hospital, with a very unlucky number.
When Ramanjam enquired what the number was, Prof. Hardy
replied: 1729.
Ramanujam’s face lit up with a smile and he said that it was
not an unlucky number at all, but a very interesting number, the only number
that can be represented as the sum of two cubes in two different ways!
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