Definition:Taxicab Number/Historical Note
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Historical Note on Taxicab Number
The first person to find an integer with this property was Bernard Frénicle de Bessy in $1657$.
He discovered $5$ instances of these numbers in response to a challenge by Leonhard Paul Euler:
| \(\ds 1729\) | \(=\) | \(\, \ds 10^3 + 9^3 \, \) | \(\, \ds = \, \) | \(\ds 12^3 + 1^3\) | ||||||||||
| \(\ds 4104\) | \(=\) | \(\, \ds 15^3 + 9^3 \, \) | \(\, \ds = \, \) | \(\ds 16^3 + 2^3\) | ||||||||||
| \(\ds 39 \, 312\) | \(=\) | \(\, \ds 15^3 + 33^3 \, \) | \(\, \ds = \, \) | \(\ds 34^3 + 2^3\) | ||||||||||
| \(\ds 40 \, 033\) | \(=\) | \(\, \ds 16^3 + 33^3 \, \) | \(\, \ds = \, \) | \(\ds 34^3 + 9^3\) | ||||||||||
| \(\ds 20 \, 683\) | \(=\) | \(\, \ds 24^3 + 19^3 \, \) | \(\, \ds = \, \) | \(\ds 27^3 + 10^3\) |
The name taxicab number arises from an anecdote related by G.H. Hardy about a visit to Srinivasa Ramanujan in hospital in a taxicab whose number was $1729$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1729$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1729$