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From: John on 15 Jun 2010 20:05
Hi,
I need to prove that there is no 4 consecutive natural numbers such
that each of them is sum of two squares.
Can you give me some hint ?

Thanks.
From: Chip Eastham on 15 Jun 2010 20:56
On Jun 15, 8:05 pm, John <to1m...(a)yahoo.com> wrote:
> Hi,
> I need to prove that there is no 4 consecutive natural numbers such
> that each of them is sum of two squares.
> Can you give me some hint ?

Consider that squares mod 4 are congruent either
to 0 or 1. What are the possible congruences
for a sum of two squares mod 4? Can these be
residues mod 4 of four consecutive natural numbers?

regards, chip
From: John on 16 Jun 2010 04:01
On Jun 16, 3:56 am, Chip Eastham <hardm...(a)gmail.com> wrote:
> On Jun 15, 8:05 pm, John <to1m...(a)yahoo.com> wrote:
>
> > Hi,
> > I need to prove that there is no 4 consecutive natural numbers such
> > that each of them is sum of two squares.
> > Can you give me some hint ?
>
> Consider that squares mod 4 are congruent either
> to 0 or 1.  What are the possible congruences
> for a sum of two squares mod 4?  Can these be
> residues mod 4 of four consecutive natural numbers?
>
> regards, chip

Thank you.
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