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Re: modular arithmetic (in finite field - part of elliptic curves)

• To: mathgroup at smc.vnet.net
• Subject: [mg84758] Re: [mg84747] modular arithmetic (in finite field - part of elliptic curves)
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 12 Jan 2008 05:22:45 -0500 (EST)
• References: <200801120315.WAA19581@smc.vnet.net> <3084F2D8-A153-4905-AE7C-F0F4EBFB65AF@mimuw.edu.pl>

On 12 Jan 2008, at 14:50, Andrzej Kozlowski wrote:

>
> On 12 Jan 2008, at 12:15, Peppy wrote:
>
>> Part of my calculations give me
>> 11/20 mod 23
>>
>> How can this be expressed as a whole number?
>>
>> I know 1/20 mod 23 = 15
>> seeing that 15 * 20 mod 23 = 1 (inverse mod mult)
>>
>> Just wondering if it'd be 11 * 15 mod 23 which is 4?
>>
>
> One way:
>
> Mod[11*PowerMod[20, -1, 23], 23]
> 4
>
> Anoter way:
>
> Solve[{x*20 == 11, Modulus == 23}, x, Mode -> Modular]
> {{Modulus -> 23, x -> 4}}
>
> Yet another way:
>
> Reduce[x*20 == 11, x, Modulus -> 23]
> x == 4
>
>
> and so on ....
>
>
> Andrzej Kozlowski


On further thought: among the very large number of eseenitally  
equivalent methods the one that I like best is:

Det[{{11/20}}, Modulus -> 23]
4

Andrzej Kozlowski

• References:
  • modular arithmetic (in finite field - part of elliptic curves)
    • From: Peppy <BrenOMahony@gmail.com>