How to interpret 3^3 + 4^3 + 5^3 = 6^3 ?

[josdavi]

I found a special equation about 29 years ago (with a FORTRAN Program) -
3**3 + 4**3 + 5**3 = 6**3

I was/am not a mathematician, not able to fully understand the meaning behind this equation, maybe someone can derive some useful ideas like Pythagoras' theorem.

Is this equation related to 4-D objects ?

[MathematicalPhysicist]

i think euler found the same thing (im not sure).

[jcsd]

That equation has been known for a long time, it' simlair to 3^2 + 4^2 = 5^2 (which is very useful when using pythagoras' theorum) and the like, but in three dimensions.

Obviuosly it is useful in any formula that uses x^3 + y^3 + z^3

[MathematicalPhysicist]

btw if you are interested in equations of that sort like this one:a1k+ a2k+ ... + amk = b1k+ b2k+ ... + bnk k-exponent n,m-indicators you have this website:http://euler.free.fr/index.htm