[GAP Forum] A problem simplified

[Marco Costantini]

Dear Dursun Bulutoglu,
try the following code:

for p in [ 3, 5, 7, 11, 13, 17, 19, 23, 29 ] do
  F := GaloisField( p );
  x := PrimitiveRoot( F );
  u := One( F );
  A := List( [1..(p-1)/2], a -> u*a );
  B := List( [0..(p-3)/2], a -> x^a );
  Print (p, " ",  Set(A) = Set(B), "\n" );
od;

It produces:

3 true
5 true
7 true
11 false
13 false
17 false
19 false
23 false
29 false

Best regards,
Marco Costantini

On Tuesday 11 January 2005 21:43, Bulutoglu Dursun A Civ AFIT/ENC wrote:

> 	I reduced my problem to the following simpler problem:
> 	Let Z_p={0,1,2,...p-1} be the finite field with p elements and x
> be a primitive element.
> 	Also let A={1,2,3,...,(p-1)/2} and B={1,x,x^2,...,x^(p-3)/2} be
> subsets of Z_p^* then A can not be equal to B for p>7.
> 	I was wondering if you have any ideas how this could be solved.