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Hardy-Ramanujan Number

The smallest nontrivial Taxicab Number, i.e., the smallest number representable in two ways as a sum of two Cubes. It is given by


The number derives its name from the following story G. H. Hardy 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


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.

© 1996-9 Eric W. Weisstein