Abstract
In a conversation with Ramanujan, G.H. Hardy mentioned that 1729 seemed to be a dull number. Ramanujan answered, “No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.” He also stated that the answer to the corresponding problem for fourth powers “... must be very large.” In this paper, this problem and other generalizations to higher powers and larger sums is examined.
In particular, the computational results of Lander, Parkin and Selfridge (“... Equal Sums of Like Powers”) are extended.
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End behavior of Ramanujan’s Taxicab numbers
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This paper is dedicated to my teacher, Professor Emil Grosswald, in honor of his sixty-eighth birthday.
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© 1981 Springer-Verlag
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Alter, R. (1981). Computations and generalizations on a remark of Ramanujan. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096461
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DOI: https://doi.org/10.1007/BFb0096461
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Print ISBN: 978-3-540-11173-3
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