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In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 1 3 + 12 3 = 9 3 + 10 3 , also known as the Hardy-Ramanujan number.
The th taxicab number is the smallest number representable in ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number. which is associated with a story told about Ramanujan by G. H. Hardy (Hofstadter 1989, Kanigel 1991, Snow 1993).
Feb 9, 2023 · The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).
Aug 15, 2013 · In honor of the Ramanujan-Hardy conversation, the smallest number expressible as the sum of two cubes in different ways is known as the taxicab number and is denoted as . Therefore, with this notation, we see that .
Jun 19, 2024 · A taxicab number (the definition that is being used here) is a positive integer that can be expressed as the sum of two positive cubes in more than one way. The first taxicab number is 1729, which is: 1 3 + 12 3 and also. 9 3 + 10 3. Taxicab numbers are also known as: taxi numbers. taxi-cab numbers.
A taxicab number is the name given by mathematicians to a sequence of special numbers: 2, 1729 etc. A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways.
More generally, the smallest natural number which can be expressed as the sum of n positive cubes is called the n th taxicab number. The first taxicab numbers are:
