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#### mente oscura

##### Well-known member

- Nov 29, 2013

- 172

I contribute a small study:

[tex]For : a, b, c, d, e, n \in{N} / a^3=b^3+c^3+d^3+e^3[/tex]

Family 1ª)

[tex]a=3n^6+3n^3+1[/tex]

[tex]b=3n^6+3n^3[/tex]

[tex]c=3n^4+2n[/tex]

[tex]d=n[/tex]

[tex]e=1^3[/tex]

Example:

[tex]For \ n=1 \ then: 7^3=6^3+5^3+1^3+1^3[/tex]

[tex]For \ n=2 \ then: 217^3=216^3+52^3+2^3+1^3[/tex]

[tex]For \ n=3 \ then: 2269^3=2268^3+249^3+3^3+1^3[/tex]

[tex]For \ n=4 \ then: 12481^3=12480^3+776^3+4^3+1^3[/tex]

...

Regards.

[tex][/tex]