In number theory, the generalized taxicab number is the smallest number — if it exists — 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 :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.
See also Cabtaxi number Lander, Parkin, and Selfridge conjecture
References
External links Generalised Taxicab Numbers and Cabtaxi Numbers Taxicab Numbers – 4th powers Taxicab numbers by Walter Schneider
de:Taxicab-Zahl#Verallgemeinerte Taxicab-Zahl