Henry Ernest Dudeney/Puzzles and Curious Problems/124 - Cube Differences

Puzzles and Curious Problems by Henry Ernest Dudeney: $124$

Cube Differences

If we wanted to find a way of making the number $1 \, 234 \, 567$ the difference between two squares,

we could of course write down $517 \, 284$ and $617 \, 283$ --

a half of the number plus $\tfrac 1 2$ and minus $\tfrac 1 2$ respectively to be squared.

But it will be found a little more difficult to discover two cubes the difference of which is $1 \, 234 \, 567$.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $124$. -- Cube Differences
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $197$. Cube Differences