In number theory, the generalized taxicab number is the smallest number â if it exists â that can be expressed as the sum of numbers to the th positive power in different ways. For and , they coincide with the taxicab number.
The latter example is 1729, as first noted by Ramanujan.
Euler showed that
However, is not known for any :<br>No positive integer is known that can be written as the sum of two 5th powers in more than one way, and it is not known whether such a number exists.