Hardy-Ramanujan Number/Examples/87,539,319/Mistake
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Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $87,539,319$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $87,539,319$
Mistake
- The smallest number that can be represented as the sum of $2$ cubes in $3$ different ways.
This should say:
- The smallest number that can be represented as the sum of $2$ positive cubes in $3$ different ways.
This is because we have that $4104$ is the smallest natural number which can be expressed as the sum of $2$ cubes in $3$ different ways:
\(\ds 4104\) | \(=\) | \(\ds 16^3 + 2^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 15^3 + 9^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {-12}^3 + 18^3\) |
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $87,539,319$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $87,539,319$