PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: Very low
[parent] cabtaxi number (Definition)

A cabtaxi number for a given $ n$ is the smallest positive number which can be written as $ a^3 + b^3$ in $ n$ different ways, with either $ a$ or $ b$ allowed to be negative integers. For example, 91 is the 2nd cabtaxi number since it can be expressed $ (-5)^3 + 6^3 = 3^3 + 4^3 = 91$. The known cabtaxi numbers are 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, listed in A047696 of Sloane's OEIS. Adding the restriction $ a \geq b > 0$ gives the definition for the taxicab numbers.



"cabtaxi number" is owned by PrimeFan.
(view preamble)

View style:


This object's parent.
Log in to rate this entry.
(view current ratings)

Cross-references: taxicab numbers, restriction, OEIS, integers, negative, number, positive
There is 1 reference to this entry.

This is version 1 of cabtaxi number, born on 2008-03-21.
Object id is 10432, canonical name is CabtaxiNumber.
Accessed 154 times total.

Classification:
AMS MSC00A08 (General :: General and miscellaneous specific topics :: Recreational mathematics)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)