Hardy-Ramanujan Number/Examples/87,539,319/Mistake

Source Work

The Dictionary

$87,539,319$

The Dictionary

$87,539,319$

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 $

$=$

$\ds \paren {-12}^3 + 18^3$