Cubes Again [Resolved]

[fundu]

This is just a sequel to a recent problem which ended by the Fermat's theorem.

Find the smallest number which can be expressed as the sum of cubes of two natural numbers in two different ways?

Thus if the number to find is x, then

x = a**3 + b**3 = c**3 + d**3

where a, b, c and d are natural numbers.

Definitely you are required to find a, b, c and d as well.

Problem courtsey the great mathematician Ramanujam, who was the friend of every number. There is a little story on this number occured while he was in hospital on the last day of his life.

[jemidiah]

1, 12, 9, 10, respectively. I brute forced it (ie, programmed it)

[sql_lall]

There are story's behind this number too:

1) Aparently, one day a male mathematian (not sure the name) was going to see Ramanujan to talk about maths stuff.
Anyway, on the way up, the man saw a car numberplate with the number 1729 on it.
While talking, Ramanujan was saying how every number is interesting in a mathematical sense, and the man made a passing comment that the number he saw, 1729, was rather uninteresting.
To this, Ramanujan was shocked, immediately exclaiming how 1729 was the first number that could be written as the sum of two cubes in two ways!

2) (From Proof, by David Auburn) A Father/Daughter are talking, both mathematically talented. The Daughter mentions how she's wasted about a month of her life. The Father asks exactly how much, to which the daughter replys 'about 33 days'. He then asks EXACTLY how much. She catches on, and says 33 1/4. He plays along and asks why thats special, and then goes on to say that if every day was a year, then she'd have wasted 1729 days. She the joins in, reciting 1729, the first number expressable as the sum of two cubes in two different ways...

So, you see, 1729 is an interesting number