Generalized taxicab number
- 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.
It has been shown by Euler that
:
However, "Taxicab"(5, 2, "n") is not known for any "n" ≥ 2; No positive integer is known at all which can be written as the sum of two fifth powers in more than one way.
External links
* [http://web.archive.org/web/20050425023736/http://www.wschnei.de/number-theory/taxicab-numbers.html Walter Schneider: Taxicab numbers]
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