Puzzles- contd

[Benny Lava]

Some more words of Ramanujan as hint:

Ramanujan: No Hardy! It is the smallest number that can be expressed as the sum of two___________________

Hardy: I rode in a taxi with the number 1729. An ordinary number

Ramanujan: No Hardy! It is a special number. It is the smallest number that can be exppressed as.............................

Fill in the blanks!

( Don't search the internet or run to the libray/bookstore for books on Ramanujan! )

I have heard this story before, but waiting for someone to answer

[GP]

naanum andha story kaelvi pattirukaen.
anyway one more specialty of the number 1729
1+7+2+9=19
multiply 19 by its reverse digit
i.e. 19 X 91 = 1729

[sathya_1979]

sum of 2 different sets of cubes:
10 power 3 + 9 power 3 = 1000 + 729 = 1729
12 power 3 + 1 power 3 = 1728 + 1 = 1729

[rajraj]

sum of 2 different sets of cubes:
10 power 3 + 9 power 3 = 1000 + 729 = 1729
12 power 3 + 1 power 3 = 1728 + 1 = 1729

Correct! 1729 is the smallest number that can be expressed as the sum of two cubes in two different ways !