[seqfan] Re: 1^5+2^5+...+n^5 is a square

Ignacio Larrosa Cañestro ilarrosa at mundo-r.com
Mon Oct 22 18:15:41 CEST 2012


El 22/10/2012 16:23, Charles Greathouse escribió:
> It was recently asked (on MathOverflow, I think) whether the formula on A031138:
>
> a(n) =11*(a(n-1)-a(n-2)) + a(n-3)
>
> was proved or merely conjectural. Of course it should be proved to be
> included as it is, but would someone verify this?
>
> This is of course a 6th-degree Diophantine equation:
>
> 12m^2 = n^2 (n+1)^2 (2n^2 + 2n - 1)
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

This is easy , the diofantic is actually quadratic:

In order to

n^2(n+1)^2(2n^2 + 2n - 1)/12

be a square, it is sufficient with that

(2n^2 + 2n - 1)/12 = m^2

And it is certainly a quadratic, and trivial, quadratic diophantic equation.

-- 
Saludos,

Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosa at mundo-r.com
http://www.xente.mundo-r.com/ilarrosa/GeoGebra/




More information about the SeqFan mailing list