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/