The nth taxicab number, denoted Ta(n), is the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The best known example is 1729, the Hardy-Ramanujan number, which is Ta(2) because it equals both 1 cubed plus 12 cubed and 9 cubed plus 10 cubed. Taxicab numbers are studied in number theory as an illustration of how the same integer can arise from different combinations of cubes.
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Source Wolfram MathWorld: Taxicab Number
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Source Bernard Frénicle de Bessy (Wikipedia)
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1. Taxicab Number (Wikipedia)
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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.
Bernard Frénicle de Bessy (Wikipedia)
Principal Result Of: Bernard Frénicle de Bessy, Lead, principal resultQuote, Principal Result Of: Bernard Frénicle de Bessy, Lead, principal result
He solved many problems created by Fermat and also discovered the cube property of the number 1729 (Ramanujan number), later referred to as a taxicab number.
Wolfram MathWorld: Taxicab Number
Wolfram MathWorldIn Branch: Number Theory, Subject classificationsQuote, In Branch: Number Theory, Subject classifications
Number Theory Special Numbers
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