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Re: Congruences

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29008] Re: [mg29007] Congruences
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Fri, 25 May 2001 01:47:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 01.5.24 5:07 PM, Flip at nospam at newsranger.com wrote:

> Hi All,
> 
> I was having a difficult time find this in the documentation and was hoping
> someone here could help.
> 
> 1.  How do you solve the congruence 19 x = 1 mod 140?
> 
> 2.  I am trying to verify that x = 12 mod 16 (where x is a 1024-bit number).
> How do I do that (essentially the same as question 1.)?
> 
> Thank you ... Flip
> 
> 
> 

Method 1:

In[3]:=
Solve[{19*x == 1, Modulus == 140}, x, Mode -> Modular]

Out[3]=
{{Modulus -> 140, x -> 59}}

Method 2:

In[5]:=
PowerMod[19,-1,140]

Out[5]=
59

I am puzzled by your second question. Have you tried Mod[x,16]? (Or,  if x
is given in the form a^n:  PowerMod[a,n,16]).
-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/~andrzej/



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