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Comment by namanyayg | Hacker News Reader

Hardy just saw it on a taxi cab and expressed sadness; Ramanujam pointed out the mathematical beauty of the number.

The real question is, did he know of this fact already or did he come up with it on the spot after hearing what Hardy said?

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I suspect he knew it already. It kind of stands out as an almost-repeated digit pattern if you look at a table of cubes (in base 10), as the cube sums concerned are 10³+9³ = 1000+729 and 12³+1³ = 1728+1. Showing that it's the smallest such number is not difficult, but would take a bit of thought to come up with on the spot. You can do it by checking a few combinations of terms from your table:

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