Example 3.2.11 Order .sagews

for a in [1..4]:
    (a,a^2,mod(a^2,5))

(1, 1, 1) (2, 4, 4) (3, 9, 4) (4, 16, 1)

p=5;
(p-1)/2;
for a in [1..(p-1)]:
    (a,a^2,mod(a^((p-1)/2),p))

2 (1, 1, 1) (2, 4, 4) (3, 9, 4) (4, 16, 1)

p=7;
(p-1)/2;
for a in [1..(p-1)]:
    (a,a^((p-1)/2),mod(a^((p-1)/2),p))

3 (1, 1, 1) (2, 8, 1) (3, 27, 6) (4, 64, 1) (5, 125, 6) (6, 216, 6)

p=11;
(p-1)/2;
for a in [1..(p-1)]:
    (a,a^2,mod(a^((p-1)/2),p))

5 (1, 1, 1) (2, 4, 10) (3, 9, 1) (4, 16, 1) (5, 25, 1) (6, 36, 10) (7, 49, 10) (8, 64, 10) (9, 81, 1) (10, 100, 10)