Re: For Fermat fans
From: William Elliot (marsh_at_privacy.net)
Date: 03/08/05
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Date: Tue, 8 Mar 2005 04:08:08 -0800
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)
76 = 36 (mod 40)
76 = x^2 + y^2 + z^2 + t^2
x, y, z, t = +-3, +-37, +-77
Nope, not possible.
Whew, I don't win.
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