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MathGroup Archive 2003

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Complex Numbers Over Fields

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39897] Complex Numbers Over Fields
  • From: "flip" <flip_alpha at safebunch.com>
  • Date: Tue, 11 Mar 2003 02:36:01 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

Is there any way to show symbolically that over the Field F{31^2}, the
expression
 
(c + d I)^32 = c^2 + d^2
 
is true.  I am asking because I have this expression in that field:
 
[(1 + 19 I)^209
 
and I can do: Mod[(1 + 19 i)^209, 31] = 26 + 28 i (the result I am looking
for).
 
But I was wondering if it can be shown after verifying the identity above by
hand?
 
Thanks for any input, Flip
 
Note: Remove "_alpha" to email me.


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