p = 3 Here the gamma-values gamma[1], gamma[2], gamma[3], gamma[4], `...` alternate 1, 2, 1, 2, `...` 

 

 

 

>    M := 2:

   p := 3:

bound := 6:

 for alpha to bound do

          GF||alpha := PI(p^alpha, M, 1):
         ord||alpha := order(GF||alpha, p^alpha):
      
od: print(``);

print(array([

['p', ``, 'alpha', ``, ``, 'p^alpha', ``, ``, '(({p^alpha-1}/2))[p]!', ORDER],

seq([p, ``, alpha, ``, ``, ifactor(p^alpha), ``, ``, GF||alpha, ord||alpha],

alpha = 1..bound)])): print(``);

lprint(`See how the factorial values alternate 1, -1, 1, -1, ... .`); print(``);

lprint(`Of course the order values alternate 1, 2, 1, 2, ... .`);
 

 

 

 

 

 

array( 1 .. 7, 1 .. 10, [( 3, 2 ) = (``), ( 5, 2 ) = (``), ( 4, 6 ) = (`*`(`^`(``(3), 3))), ( 7, 9 ) = (-1), ( 5, 3 ) = (4), ( 7, 4 ) = (``), ( 5, 9 ) = (-1), ( 5, 10 ) = (2), ( 4, 1 ) = (3), ( 7, 10 ...
`See how the factorial values alternate 1, -1, 1, -1, ... .`
`Of course the order values alternate 1, 2, 1, 2, ... .`
 

>