Henry Ernest Dudeney/Puzzles and Curious Problems/129 - Squares and Cubes/Solution

by : $129$

 * Squares and Cubes
 * Find two different numbers such that the sum of their squares shall equal a cube, and the sum of their cubes equals a square.

Solution
We have:


 * $625^2 + 1250^2 = 125^3$

while:
 * $625^3 + 1250^3 = 46 \, 875^2$