(11:25) gp > for(n=1,10000,if(eulerphi(n)==8,print(n)))
15
16
20
24
30
---
(12:11) gp > factormod(x^3-1,2)
%1 = 
[                Mod(1, 2)*x + Mod(1, 2) 1]

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

(12:11) gp > factormod(x^3-x-1,2)
%2 = 
[Mod(1, 2)*x^3 + Mod(1, 2)*x + Mod(1, 2) 1]
---
(16:48) gp > x=[1,1,0;0,1,0;0,0,1]
%1 = 
[1 1 0]

[0 1 0]

[0 0 1]

(16:49) gp > y=[1,0,0;0,1,1;0,0,1]
%2 = 
[1 0 0]

[0 1 1]

[0 0 1]

(16:50) gp > x*y/x/y
%3 = 
[1 0 1]

[0 1 0]

[0 0 1]

(16:50) gp > z=x*y/x/y
%4 = 
[1 0 1]

[0 1 0]

[0 0 1]

(16:50) gp > x*z/x
%5 = 
[1 0 1]

[0 1 0]

[0 0 1]

(16:50) gp > y*z/y
%6 = 
[1 0 1]

[0 1 0]

[0 0 1]

(16:50) gp > x*z==z*x
%7 = 1
(16:50) gp > y*z==z*y
%8 = 1
(16:50) gp > x^2
%9 = 
[1 2 0]

[0 1 0]

[0 0 1]

(16:50) gp > x^3
%10 = 
[1 3 0]

[0 1 0]

[0 0 1]

(16:50) gp > z^2
%11 = 
[1 0 2]

[0 1 0]

[0 0 1]

(18:46) gp > factormod(x^3-x-1,2)
%1 = 
[Mod(1, 2)*x^3 + Mod(1, 2)*x + Mod(1, 2) 1]

(18:47) gp > factormod(x^3-x^2-1,2)
%2 = 
[Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2) 1]

(18:48) gp > factormod(x^3-x^2-x-1,2)
%1 = 
[Mod(1, 2)*x + Mod(1, 2) 3]

%19 = 
[10  6  6]

[27 17 14]

[32 20 16]

(19:19) gp > matdet(%)
%20 = -8
(19:19) gp > snf(%19)
%21 = [4, 2, 1]
(19:28) gp > factormod(x^4-x,2)
%36 = 
[                            Mod(1, 2)*x 1]

[                Mod(1, 2)*x + Mod(1, 2) 1]

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

(19:30) gp > factormod(x^9-x,2)
%37 = 
[            Mod(1, 2)*x 1]

[Mod(1, 2)*x + Mod(1, 2) 8]

(19:30) gp > factormod(x^6-x,2)
%38 = 
[                                                            Mod(1, 2)*x 1]

[                                                Mod(1, 2)*x + Mod(1, 2) 1]

[Mod(1, 2)*x^4 + Mod(1, 2)*x^3 + Mod(1, 2)*x^2 + Mod(1, 2)*x + Mod(1, 2) 1]