4.1.18 Fermat's Little Theorem.sagews

p=5;
for a in [0..(p-1)]:
    a,a^p,mod(a^p,p)

(0, 0, 0) (1, 1, 1) (2, 32, 2) (3, 243, 3) (4, 1024, 4)

p=6;
for a in [0..(p-1)]:
    a,a^p,mod(a^p,p)

(0, 0, 0) (1, 1, 1) (2, 64, 4) (3, 729, 3) (4, 4096, 4) (5, 15625, 1)

p=7;
for a in [0..(p-1)]:
    a,a^p,mod(a^p,p)

(0, 0, 0) (1, 1, 1) (2, 128, 2) (3, 2187, 3) (4, 16384, 4) (5, 78125, 5) (6, 279936, 6)

p=11;
for a in [0..(p-1)]:
    a,a^p,mod(a^p,p)

(0, 0, 0) (1, 1, 1) (2, 2048, 2) (3, 177147, 3) (4, 4194304, 4) (5, 48828125, 5) (6, 362797056, 6) (7, 1977326743, 7) (8, 8589934592, 8) (9, 31381059609, 9) (10, 100000000000, 10)

p=13;
for a in [0..(p-1)]:
    a,a^p,mod(a^p,p)

(0, 0, 0) (1, 1, 1) (2, 8192, 2) (3, 1594323, 3) (4, 67108864, 4) (5, 1220703125, 5) (6, 13060694016, 6) (7, 96889010407, 7) (8, 549755813888, 8) (9, 2541865828329, 9) (10, 10000000000000, 10) (11, 34522712143931, 11) (12, 106993205379072, 12)