I found an identity form: $x_1^3+x_2^3+x_3^3+x_4^3=y_1^3+y_2^3+y_3^3+y_4^3$ as follows: $$(a+b+c)^3+a^3+b^3+c^3=(a+b)^3+(b+c)^3+(c+a)^3+(6y)^3$$

Where $abc=36y^3$

Poof of this identity is very simple. But the identity nice.

Which reference of the identity? can generalized of the identity?


1 Answer 1


Equation (shown below) has parametrization:



For $k=2$, we get: $(3,12,64,79)^3=(15,24,67,76)^3$


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