Re: Odd thing about a^4+b^4+c^4+d^4+e^4=f^4
- From: john_ramsden@xxxxxxxxxxxxxx
- Date: 24 Sep 2005 04:15:55 -0700
titus_piezas@xxxxxxxxx wrote:
>
> The smallest solution to the equation in the title is
> 2^4+2^4+3^3+4^4+4^4=5^4. It turns out that distinct solutions
> tend to sum up to the _same_ number again and again. Any ideas
> why this is the case? See details in:
>
> http://www.geocities.com/titus_piezas/clustering.html
Hmm, interesting. Is there any sign of this when some or all
the terms are only squares?
I guess one can compose a sum of eight squares a_i^2 with itself
to obtain an octonian "sum of eight squares equal to a square"
identity, and equating three terms to zero might be linear in
three of the a_i, giving a "sum of five squares equal square"
identity, which could have some symmetries.
.
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