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primitive root
09-01-2015, 01:28 PM
Post: #1
primitive root
function next_primitive_root(n,p) returns the smallest primitive root of "p" that is larger than "n"

example:

next_primitive_root(5, 13) returns 6
next_primitive_root(Ans,13) returns 7
<enter> returns 11
<enter> returns "no primitive roots exist"

Code:
#pragma mode( separator(.,;) integer(h32))

EXPORT next_primitive_root(n,p)
BEGIN
 local a,b,c,j,k;
 a:=euler(p);
 b:=ifactors(a);
 c:=length(b);
 for j from n+1 to p−1 do
  for k from 1 to c step 2 do
   if powmod(j,a/b(k),p) == 1 then
    break;
   end;
   if (k == c-1) and (gcd(j,p)==1) then
    return j;
   end;
  end;
 end;
 return "no primitive roots exist";
END;
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