Cabtaxi number
Encyclopedia
In mathematics
, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive integer
that can be written as the sum of two positive or negative or 0 cubes in n ways. Such numbers exist for all n (since taxicab number
s exist for all n); however, only 10 are known :
Cabtaxi(5), Cabtaxi(6) and Cabtaxi(7) were found by Randall L. Rathbun; Cabtaxi(8) was found by Daniel J. Bernstein
; Cabtaxi(9) was found by Duncan Moore, using Bernstein's method. Cabtaxi(10) was first reported as an upper bound by Christian Boyer in 2006 and verified as Cabtaxi(10) by Uwe Hollerbach and reported on the NMBRTHRY mailing list on May 16, 2008.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
that can be written as the sum of two positive or negative or 0 cubes in n ways. Such numbers exist for all n (since taxicab number
Taxicab number
In mathematics, the nth taxicab number, typically denoted Ta or Taxicab, is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways. The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th...
s exist for all n); however, only 10 are known :
Cabtaxi(5), Cabtaxi(6) and Cabtaxi(7) were found by Randall L. Rathbun; Cabtaxi(8) was found by Daniel J. Bernstein
Daniel J. Bernstein
Daniel Julius Bernstein is a mathematician, cryptologist, programmer, and professor of mathematics at the University of Illinois at Chicago...
; Cabtaxi(9) was found by Duncan Moore, using Bernstein's method. Cabtaxi(10) was first reported as an upper bound by Christian Boyer in 2006 and verified as Cabtaxi(10) by Uwe Hollerbach and reported on the NMBRTHRY mailing list on May 16, 2008.