Hardy-Ramanujan: $1729 = 1^{3} + 12^{3} = ?^{3} + ?^{3}$

Hardy-Ramanujan: $1729 = 1^{3} + 12^{3} = ?^{3} + ?^{3}$
  1. $9^{3} + 10^{3}$
  2. $8^{3} + 11^{3}$
  3. $7^{3} + 12^{3}$
  4. $6^{3} + 13^{3}$

Solution

$9^{3} + 10^{3} = 729 + 1000 = 1729$.

Asked in: IMO

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