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Topic: ----------- math reference
Replies: 3   Last Post: Aug 10, 2011 6:29 PM

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Ulrich D i e z

Posts: 19
Registered: 1/2/10
Re: ----------- math reference
Posted: Aug 10, 2011 6:29 PM
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I wrote:

> How about justifying a slight variant of the above statement:
>
> Statement: Every integer N that is 2 (mod 4) cannot be
> expressed as the difference of two squares.


Of course the statement can be verified in a more easy
way - I don't know what I was thinking/I doubt I was
thinking at all:

Squares are 0 or 1 (mod 4) while
[0 or 1 (mod 4)] - [0 or 1 (mod 4)] =
0-0=1-1=0 or 1-0=1 or 0-1=-1=3 (mod 4) =/= 2 (mod 4).

Ulrich



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