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The smallest nontrivial Taxicab Number, i.e., the smallest number representable in two ways as a sum of two
Cubes. It is given by
told about Ramanujan.
``Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered
the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared,
`rather a dull number,' adding that he hoped that wasn't a bad omen. `No, Hardy,' said Ramanujan, `it is a very interesting
number. It is the smallest number expressible as the sum of two [Positive] cubes in two different ways''' (Hofstadter
1989, Kanigel 1991, Snow 1993).
See also Diophantine Equation--Cubic, Taxicab Number
References
Guy, R. K. ``Sums of Like Powers. Euler's Conjecture.'' §D1 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 139-144, 1994.
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 68,
1959.
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid.
New York: Vintage Books, p. 564, 1989.
Kanigel, R. The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Washington Square Press, p. 312, 1991.
Snow, C. P. Foreword to Hardy, G. H.
A Mathematician's Apology, reprinted with a foreword by C. P. Snow.
New York: Cambridge University Press, p. 37, 1993.