Can you add any two cubes to get a cube?
Can you add any two cubes to get a cube?
Imagine you're stacking blocks in a pyramid shape. You know that if you stack 1 block on top of 2 blocks, you get a 3-block tall pyramid. But what if you tried stacking 1 block, 2 blocks, and 3 blocks to make a 4-block tall pyramid?
Fermat's Last Theorem tells us that there's no way to stack cubes in such a way that the height of the pyramid equals the cube of the total number of blocks. The technical term is xⁿ + yⁿ = zⁿ for n > 2.
Example
If you stack 1 block (1³), 2 blocks (2³), it makes 9 blocks (3³). But there's no way to stack 1, 2, and 3 blocks to make a 4-block tall pyramid.
Remember this
No three cubes can be added to form a fourth cube.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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