The nth taxicab number, denoted as T(n), is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways (source: wikipedia).
Example:
T(1) = 2 = 1^3 + 1^3
T(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3Return the value of n if the given number is a taxicab number. Return 0 if not. If the input is 1729, output would be 2, since 1729 is smallest number that can be expressed as a sum of two cubes in two (n=2) distinct ways.
Avoid look up table solution. Test suit might expand.
not a general solution
Considering that the proof of the 6th taxicab number produced over 8GB of data and consisted of an exhaustive search over the integers up to 1e21, a truly generic solution is not really possible.
:-)
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