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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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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.
Wolfram MathWorld: Taxicab Number
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Number Theory Special Numbers
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