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1.
The first natural number than can be expressed as the sum of two cubes in two different ways:

9^3 + 10^3 = 729 + 1000 = 1729
1^3 + 12^3 = 1 + 1728 = 1729
Someone: Did you know that 1729 = 9^3+10^3 = 1^3+12^3?
Me: Yes.
by dav0rd July 08, 2005