Taxicab number
Smallest integer expressable as a sum of two positive integer cubes in n distinct ways / From Wikipedia, the free encyclopedia
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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.[1] The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103, also known as the Hardy-Ramanujan number.[2][3]
The name is derived from a conversation ca.ā1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy:
I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways."[4][5]