       Re: polynomial congruence

• To: mathgroup at smc.vnet.net
• Subject: [mg26145] Re: [mg26138] polynomial congruence
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Thu, 30 Nov 2000 01:03:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```As long as p is not very large it is easy to do.  For example, suppopse you
want to solve all the congruences

In:=
f[x_, y_] := x^2 + y^2 - 25

In:=
Table[Solve[{f[x, y] == 0, Modulus == 11}[], x], {y, 0, 10}]

Out=
{{{x -> -5}, {x -> 5}}, {{x -> -2 Sqrt},

{x -> 2 Sqrt}}, {{x -> -Sqrt}, {x -> Sqrt}},

{{x -> -4}, {x -> 4}}, {{x -> -3}, {x -> 3}},

{{x -> 0}, {x -> 0}}, {{x -> -I Sqrt},

{x -> I Sqrt}}, {{x -> -2 I Sqrt},

{x -> 2 I Sqrt}}, {{x -> -I Sqrt},

{x -> I Sqrt}}, {{x -> -2 I Sqrt},

{x -> 2 I Sqrt}},

{{x -> -5 I Sqrt}, {x -> 5 I Sqrt}}}

Note that these answers really lie in the algebraic closure of the finite
filed Z/11.

on 11/28/00 3:56 PM, Constantinos Draziotis at roth at math.auth.gr wrote:

>
> Hello,i am a new user of mathematica,i will appreciate very much if you
> can help me with this(it seems simple) problem:i want to solve a
> polynomial congruence modulo prime number i.e f(x,y)=0modulo(p)(prime
> number) with y=0,1,2,3...,n (n:integer).i have to find the classes
> xmodulo(p)
>