Taxicab Number
Number Theory
Level
2
Which is the smallest number expressible as a sum of two cubes in two different ways ?
1729
13882
20683
4104
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1 solution
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth 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.
1729 is known as the Hardy–Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation " I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." ” The two different ways are:
1729 = 12 cubed+ 1 cubed 1729 = 13 cubed.
Related article in Wiki : https://en.wikipedia.org/wiki/Taxicab_number