arara:# gp
               GP/PARI CALCULATOR Version 2.12.1 (development 25142-46eb34041)
                 i386 running darwin (x86-64/GMP-6.2.0 kernel) 64-bit version
            compiled: Mar 22 2020, Apple clang version 11.0.0 (clang-1100.0.33.17)
                                   threading engine: single
                        (readline v8.0 enabled, extended help enabled)

                            Copyright (C) 2000-2020 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY 
WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
? ?
Help topics: for a list of relevant subtopics, type ?n for n in
   0: user-defined functions (aliases, installed and user functions)
   1: PROGRAMMING under GP
   2: Standard monadic or dyadic OPERATORS
   3: CONVERSIONS and similar elementary functions
   4: functions related to COMBINATORICS
   5: NUMBER THEORETICAL functions
   6: POLYNOMIALS and power series
   7: Vectors, matrices, LINEAR ALGEBRA and sets
   8: TRANSCENDENTAL functions
   9: SUMS, products, integrals and similar functions
  10: General NUMBER FIELDS
  11: Associative and central simple ALGEBRAS
  12: ELLIPTIC CURVES
  13: L-FUNCTIONS
  14: MODULAR FORMS
  15: MODULAR SYMBOLS
  16: GRAPHIC functions
  17: The PARI community
Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)
Extended help (if available):
  ??             (opens the full user's manual in a dvi previewer)
  ??  tutorial / refcard / libpari (tutorial/reference card/libpari manual)
  ??  refcard-ell (or -lfun/-mf/-nf: specialized reference card)
  ??  keyword    (long help text about "keyword" from the user's manual)
  ??? keyword    (a propos: list of related functions).
? ?znprimroot
znprimroot(n): returns a primitive root of n when it exists.

? ??znprimroot

? znprimroot(2)
%1 = Mod(1, 2)
? znprimroot(3)
%2 = Mod(2, 3)
? znprimroot(4)
%3 = Mod(3, 4)
? znprimroot(5)
%4 = Mod(2, 5)
? vector(4,n,Mod(2^n,5))
%5 = [Mod(2, 5), Mod(4, 5), Mod(3, 5), Mod(1, 5)]
? liftint(%)
%6 = [2, 4, 3, 1]
? poderes(x,p) = liftint(vector(p,n,Mod(x,p)^n))
%7 = (x,p)->liftint(vector(p,n,Mod(x,p)^n))
? poderes(2,5)
%8 = [2, 4, 3, 1, 2]
? poderes(2,6)
%9 = [2, 4, 2, 4, 2, 4]
? poderes(5,6)
%10 = [5, 1, 5, 1, 5, 1]
? 25 == 1+4*6
%11 = 1
? poderes(2,7)
%12 = [2, 4, 1, 2, 4, 1, 2]
? a= Mod(2,7)
%13 = Mod(2, 7)
? a^2
%14 = Mod(4, 7)
? a^3
%15 = Mod(1, 7)
? 2^3 == Mod(1,7)
%16 = 1
? Mod(2,7)^3 == 1
%17 = 1
? "Então 2 não é gerador de grupo multiplicativo modulo 7, mas é gerador modulo 5"
%18 = "Então 2 não é gerador de grupo multiplicativo modulo 7, mas é gerador modulo 5"
? poderes(2,7)
%19 = [2, 4, 1, 2, 4, 1, 2]
? poderes(3,7)
%20 = [3, 2, 6, 4, 5, 1, 3]
? "3 é um gerador"
%21 = "3 é um gerador"
? znprimroot(5)
%22 = Mod(2, 5)
? znprimroot(7)
%23 = Mod(3, 7)
? znprimroot(8)
  ***   at top-level: znprimroot(8)
  ***                 ^-------------
  *** znprimroot: domain error in znprimroot: argument = 8
  ***   Break loop: type 'break' to go back to GP prompt
break> break

? poderes(1,8)
%24 = [1, 1, 1, 1, 1, 1, 1, 1]
? poderes(2,8)
%25 = [2, 4, 0, 0, 0, 0, 0, 0]
? poderes(3,8)
%26 = [3, 1, 3, 1, 3, 1, 3, 1]
? poderes(4,8)
%27 = [4, 0, 0, 0, 0, 0, 0, 0]
? poderes(5,8)
%28 = [5, 1, 5, 1, 5, 1, 5, 1]
? poderes(6,8)
%29 = [6, 4, 0, 0, 0, 0, 0, 0]
? poderes(7,8)
%30 = [7, 1, 7, 1, 7, 1, 7, 1]
? matrix(8,8,a,b,liftint(Mod(a^b,8)))
%31 = 
[1 1 1 1 1 1 1 1]

[2 4 0 0 0 0 0 0]

[3 1 3 1 3 1 3 1]

[4 0 0 0 0 0 0 0]

[5 1 5 1 5 1 5 1]

[6 4 0 0 0 0 0 0]

[7 1 7 1 7 1 7 1]

[0 0 0 0 0 0 0 0]

? znprimroot(9)
%32 = Mod(2, 9)
? poderes(2,9)
%33 = [2, 4, 8, 7, 5, 1, 2, 4, 8]
? znprimroot(11)
%34 = Mod(2, 11)
? znprimroot(13)
%35 = Mod(2, 13)
? vector(50,n,p=prime(n),znprimroot(p))
  ***   too many arguments: vector(50,n,p=prime(n),znprimroot(p))
  ***                                              ^--------------
? vector(50,n,p=prime(n);znprimroot(p))
%36 = [Mod(1, 2), Mod(2, 3), Mod(2, 5), Mod(3, 7), Mod(2, 11), Mod(2, 13), Mod(3, 17), Mod(2, 19), Mod(5, 23), Mod(2, 29), Mod(3, 31), Mod(2, 37), Mod(6, 41), Mod(3, 43), Mod(5, 47), Mod(2, 53), Mod(2, 59), Mod(2, 61), Mod(2, 67), Mod(7, 71), Mod(5, 73), Mod(3, 79), Mod(2, 83), Mod(3, 89), Mod(5, 97), Mod(2, 101), Mod(5, 103), Mod(2, 107), Mod(6, 109), Mod(3, 113), Mod(3, 127), Mod(2, 131), Mod(3, 137), Mod(2, 139), Mod(2, 149), Mod(6, 151), Mod(5, 157), Mod(2, 163), Mod(5, 167), Mod(2, 173), Mod(2, 179), Mod(2, 181), Mod(19, 191), Mod(5, 193), Mod(2, 197), Mod(3, 199), Mod(2, 211), Mod(3, 223), Mod(2, 227), Mod(6, 229)]
? factor(228)
%37 = 
[ 2 2]

[ 3 1]

[19 1]

? isprime(229)
%38 = 1
? 
Goodbye!