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

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The equation 3^3 + 4^3 + 5^3 = 6^3 presents a unique mathematical relationship that may have connections to higher-dimensional geometry. It draws parallels to the well-known Pythagorean theorem, 3^2 + 4^2 = 5^2, but extends the concept into three dimensions. The discussion suggests potential implications for understanding 4-D objects and references Euler's work in this area. The equation is noted for its relevance in formulas involving cubic sums. Overall, it highlights the intriguing nature of mathematical relationships across different dimensions.
josdavi
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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 ?
 
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i think euler found the same thing (im not sure).
 
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
 
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
 

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