<s>[INST] Special numbers Our teacher talked about some special numbers.
These numbers total of 2 different numbers' cube. For example :
$x^3+y^3 = z^3+t^3 = \text{A-special-number}$
What is the name of this special numbers ?
 [/INST] Here's a sample identity by Ramanujan,
$(3x^2+5xy-5y^2)^3 + (4x^2-4xy+6y^2)^3 = (-5x^2+5xy+3y^2)^3 + (6x^2-4xy+4y^2)^3$
Let {x,y} = {-1,0} and you get the nice $3^3+4^3+5^3 = 6^3$. Or {x,y} = {-1,2} for $1^3+12^3 = 9^3+10^3 = 1729$, the smallest non-trivial "taxicab number" (after transposition and removing common factors). And so on.
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