Cube of a positive integer is equivalent to 3 other positive integers cubed

Asked Sep 29 '22 at 15:26

Active Sep 29 '22 at 15:28

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How could we determine if there exists an integer d such as

$$ d^{3} = a^{3} + b^{3} + c^{3} $$

I don't need to find a,b,c. I just need to know if a solution exists for a given d. I know for example that for $a=3$, $b=4$, $c=5$ and $d=6$ the equation holds.

Thank you

edited Sep 29 '22 at 15:28

PierreCarre

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asked Sep 29 '22 at 15:26

ThePhilomath

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See this question – lulu Sep 29 '22 at 15:42
Does this answer your question? Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$ – Dietrich Burde Sep 29 '22 at 16:07
$3^3 + 4^3 + 5^3 = \color{red}{\text{what ?}}$ – user2661923 Sep 29 '22 at 16:25
https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-28/issue-4/On-Equal-Sums-of-Cubes/10.1216/rmjm/1181071714.full This paper should suffice for a complete solution. – Hersh Sep 29 '22 at 16:26
@Hersh is the pdf file of this article freely available for download, somewhere on the internet? – user2661923 Sep 29 '22 at 16:28
@user2661923 Just click on the "Download paper" Button that should be on your screen. It is free. – Hersh Sep 29 '22 at 16:32

Cube of a positive integer is equivalent to 3 other positive integers cubed

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