Legendre famously "proved" that 6 could not be the sum of the cubes of two rational numbers. Puzzlist Dudeney proved him wrong by producing two rational numbers the sum of whose cubes is 6.

Find the two rational numbers without researching Legendre or Dudeney.

(17/21)^3 + (37/21)^3 = 6

Posted by K Sengupta on 2023-04-05 00:23:23