Re: For Fermat fans
From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 03/08/05
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Date: Tue, 08 Mar 2005 18:42:45 +0000
William Elliot wrote:
> On Tue, 8 Mar 2005, Larry Hammick wrote:
>
>> Show that any positive integer which is congruent to 36 mod 40 is the sum
>> of four squares all of which are 9 mod 40.
>> The first solver wins a copy of the complete works of JSH.
>>
> 36 = x^2 + y^2 + z^2 + t^2 (mod 40)
> x = y = z = t = 9 (mod 40)
> 4*81 = 4 (mod 4). Nope, need to read as
>
> 36 = x^2 + y^2 + z^2 + t^2 (mod 40)
> x^2 = y^2 = z^2 = t^2 = 9 (mod 40)
> x, y, z, t = 3,37 (mod 40)
????
7^2 = 49 = 9 (mod 40).
Try again!
NB 76 = 49 + 9 + 9 + 9.
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Elegance is an algorithm"
Iain M. Banks, _The Algebraist_
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