> p:=2;

                                p := 2

> n:=49;

                               n := 49

> q:=p^n;

                         q := 562949953421312

> ifactor(q-1);

                        (127)  (4432676798593)

> f:=x^49+x^12+x^10+x^6+x^4+x^3+1;

                     49    12    10    6    4    3
               f := x   + x   + x   + x  + x  + x  + 1

> Irreduc(f) mod p;

                                 true

> Factor(f) mod p;

                   49    12    10    6    4    3
                  x   + x   + x   + x  + x  + x  + 1

> g:=x^5+x+1;

                                 5
                           g := x  + x + 1


> Powmod(g,127,f,x) mod p;

   48    45    44    41    38    37    36    34    31    23    22
  x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x

            21    19    17    13    8    7    2
         + x   + x   + x   + x   + x  + x  + x  + x

> Powmod(g,4432676798593,f,x) mod p;

   48    47    45    44    43    42    33    28    27    26    21
  x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x

            20    15    14    12    8    6    4    3    2
         + x   + x   + x   + x   + x  + x  + x  + x  + x  + x + 1

> Powmod(g,127*4432676798593,f,x) mod p;

                                  1

> p:=nextprime(5999847);

                             p := 5999863

> ifactor(p-1);

                        (2)  (3)  (11)  (90907)

> q:=nextprime(3901843);

                             q := 3901853

> ifactor(q-1);

                               2
                            (2)   (975463)

> n:=p*q;

                         n := 23410583446139

> phin:=(p-1)*(q-1);

                        phin := 23410573544424

> e:=17;

                               e := 17

> igcd(e,phin);

                                  1

> igcdex(e,phin,'d','tmp');

                                  1

> d;

                            9639647930057

> e*d mod phin;

                                  1

>