[GAP Forum] GAP

[Bill Allombert]

On Thu, Apr 16, 2015 at 05:35:20PM +0100, Sandeep Murthy wrote:
> 
> Once you’ve defined the variables a and p you can just do
> 
>     gap> a^p mod p = a mod p;
> 
> and
> 
>    gap> a^(p-1) mod p = 1;

I would suggest instead to do something like 
ZmodnZObj(a,p)^(p-1);
instead to avoid computing a^(p-1) as a large integer.

gap> ZmodnZObj(2,4294967297)^4294967296;
ZmodnZObj( 1, 4294967297 )
gap> time;
0
gap> 2^4294967296 mod 4294967297;
1
gap> time;
2965

Cheers,
Bill.