Taxi number

cab number

"No," he replied, "it's a very interesting number; it's the smallest number that can be expressed as the sum of two [positive] dice in two different ways."

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sspan class="mw-headline" id="Definition">Definition[edit]

Mathematically, the n-th Taxiicab number, usually Ta(n) or Taxicab(n), also known as the n-th Hardy-Ramanujan number, is the smallest number that can be summed up by two different numbers of cubes. is 1729 = Ta(2) = 13 + 123 = 93 + 103.

Its name comes from a talk around 1919 with the Mathematicians G. H. Hardy and Srinivasa Ramanujan. Like Hardy said: By 1938 G. H. Hardy and E. M. Wright had proven that such numbers existed for all integer numbers s, and their evidence could readily be transformed into a programme for generating such numbers.

Limiting addends to positives is necessary because accepting negatives allows more (and smaller) numbers to be instanced, which can be represented as totals of dice in n different ways. However, the idea of the cabin taxi number was adopted to allow for less prescriptive alternatives.

To some extent, the indication of two addends and potencies of three is also restricted; a generalised taxi cab number allows these numbers to deviate from two and three, respectively. The following six taxi cab numbers are known so far (sequence 1011541 in the OEIS): Ta (2), also known as the Hardy Ramanujan number, was first released in 1657 by Bernard Frénicle de Bessy.

Skip up ^ Quotes from G. H. Hardy, MacTutor Archived Story of Mathematics 2012-07-16 at the Wayback Machine. G. H. Hardy and E. M. Wright, An introduction to the theories of numbers, 3 nd edition, Oxford University Press, London & NY, 1954, Thm. E. Rosenstiel, J. A. Dardis and C. R. Rosenstiel, The four smallest solution in various integer positives of the diophantine formulae x3 + y3= z3 + w3= u3 + v3= me3 + me3, Bull.

D. J. Bernstein, Listing of solution for p(a) + q(b) = r(c) + s(d), Mathematics of calculation 70, 233 (2000), 389-394. Haran, Brady, ed. 1729: Taxi cabin number or Hardy-Ramanujan number. Number phile. Haran, Brady, ed. "Taxicab Numbers in Futurama." Number phile.

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