(17:10) gp > for(n=1,100,if(eulerphi(n)==4,print(n)))
5
8
10
12
(17:10) gp > polcyclo(12)
%2 = x^4 - x^2 + 1
(17:10) gp > for(n=1,100,if(eulerphi(n)==8,print(n)))
15
16
20
24
30
(17:10) gp > for(n=1,100,if(eulerphi(n)==16,print(n)))
17
32
34
40
48
60
(17:34) gp > P=x^4-x-1
%1 = x^4 - x - 1
(17:34) gp > factor(P)
%2 = 
[x^4 - x - 1 1]

(17:34) gp > factormod(P,17)
%3 = 
[                  Mod(1, 17)*x + Mod(2, 17) 1]

[                  Mod(1, 17)*x + Mod(5, 17) 1]

[Mod(1, 17)*x^2 + Mod(10, 17)*x + Mod(5, 17) 1]

(17:35) gp > poldisc(x^2+10*x+5)
%4 = 80
(17:35) gp > factor(%)
%5 = 
[2 4]

[5 1]