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Topic: Sum of squares.
Replies: 9   Last Post: Jun 8, 2008 6:25 AM

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Nathan

Posts: 188
Registered: 12/13/04
Re: Sum of squares.
Posted: Jun 7, 2008 8:05 PM
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On Jun 7, 4:10 pm, Saysero <says...@gmail.com> wrote:

> Is there m in M such that for all n in N if n>m then:
> 1) there exist k and x_1,...,x_n in N so that n=(x_1)^2 + ... +
> (x_k)^2 and
> 2) (i != j) => (x_j != x_i)
> The question is, simply put, can every number greater than some m be
> represented as a sum of unique squares.
> I hope this makes my question better understood.


A better way to say this is "distinct" instead of "unique".
The answer is yes, and m=128 is the largest exceptional value.
I worked this out by hand in 1995. It's not hard.
But for much more detail, see
http://mathworld.wolfram.com/SquareNumber.html



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