# Generalized taxicab number

In mathematics, the **generalized taxicab number** *Taxicab*(*k*, *j*, *n*) is the smallest number which can be expressed as the sum of *j* *k*th positive powers in *n* different ways. For *k* = 3 and *j* = 2, they coincide with taxicab numbers.

- - famously stated by Ramanujan.

Unsolved problem in mathematics: Does there exist any number that can be expressed as a sum of two positive fifth powers in at least two different ways, i.e.,
? (more unsolved problems in mathematics) |

Euler showed that

However, *Taxicab*(5, 2, *n*) is not known for any *n* ≥ 2; no positive integer is known which can be written as the sum of two fifth powers in more than one way.[1]

## See also

## References

- Guy, Richard K. (2004).
*Unsolved Problems in Number Theory*(Third ed.). New York, New York, USA: Springer-Science+Business Media, Inc. ISBN 0-387-20860-7.

- Ekl, Randy L. (1998). "New results in equal sums of like powers".
*Math. Comp*.**67**. pp. 1309–1315. doi:10.1090/S0025-5718-98-00979-X. MR 1474650.

## External links

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.