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Re: Congruences
*To*: mathgroup at smc.vnet.net
*Subject*: [mg29009] Re: [mg29007] Congruences
*From*: Adriano Pascoletti <pascolet at dimi.uniud.it>
*Date*: Fri, 25 May 2001 01:47:49 -0400 (EDT)
*References*: <200105240807.EAA05001@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
At 4:07 -0400 24-05-2001, Flip 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
1. You can use LinearSolve[ M, c, Modulus->p]
where M is the 1 x 1 matrix {{19}}, c the 1-dimensional vector {1} and p=140:
In[29]:= LinearSolve[{{19}},{1},Modulus->140]
Out[29]= {59}
2. Being 16=2^4 use this
FromDigits[#, 2] &[Take[IntegerDigits[x, 2], -4]] == 12
Adriano Pascoletti
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