# 數論中的偶數階Abel羣的階

U(8) ={[1]_8,[3]_8,[5]_8,[7]_8}=K_4≠C_4，
U(15)=U(3)×U(5)=C_2×C_4，
GAP命令爲：
gap> for i in [1..100] do Print("U(",i,")=",IdGroup(Units(ZmodnZ(i))),"\n"); od;
U(1)=[ 1, 1 ]
U(2)=[ 1, 1 ]
U(3)=[ 2, 1 ]
U(4)=[ 2, 1 ]
U(5)=[ 4, 1 ]
U(6)=[ 2, 1 ]
U(7)=[ 6, 2 ]
U(8)=[ 4, 2 ]
U(9)=[ 6, 2 ]
U(10)=[ 4, 1 ]
U(11)=[ 10, 2 ]
U(12)=[ 4, 2 ]
U(13)=[ 12, 2 ]
U(14)=[ 6, 2 ]
U(15)=[ 8, 2 ]
U(16)=[ 8, 2 ]
U(17)=[ 16, 1 ]
U(18)=[ 6, 2 ]
U(19)=[ 18, 2 ]
U(20)=[ 8, 2 ]
U(21)=[ 12, 5 ]
U(22)=[ 10, 2 ]
U(23)=[ 22, 2 ]
U(24)=[ 8, 5 ]
U(25)=[ 20, 2 ]
U(26)=[ 12, 2 ]
U(27)=[ 18, 2 ]
U(28)=[ 12, 5 ]
U(29)=[ 28, 2 ]
U(30)=[ 8, 2 ]
U(31)=[ 30, 4 ]
U(32)=[ 16, 5 ]
U(33)=[ 20, 5 ]
U(34)=[ 16, 1 ]
U(35)=[ 24, 9 ]
U(36)=[ 12, 5 ]
U(37)=[ 36, 2 ]
U(38)=[ 18, 2 ]
U(39)=[ 24, 9 ]
U(40)=[ 16, 10 ]
U(41)=[ 40, 2 ]
U(42)=[ 12, 5 ]
U(43)=[ 42, 6 ]
U(44)=[ 20, 5 ]
U(45)=[ 24, 9 ]
U(46)=[ 22, 2 ]
U(47)=[ 46, 2 ]
U(48)=[ 16, 10 ]
U(49)=[ 42, 6 ]
U(50)=[ 20, 2 ]
U(51)=[ 32, 16 ]
U(52)=[ 24, 9 ]
U(53)=[ 52, 2 ]
U(54)=[ 18, 2 ]
U(55)=[ 40, 9 ]
U(56)=[ 24, 15 ]
U(57)=[ 36, 5 ]
U(58)=[ 28, 2 ]
U(59)=[ 58, 2 ]
U(60)=[ 16, 10 ]
U(61)=[ 60, 4 ]
U(62)=[ 30, 4 ]
U(63)=[ 36, 14 ]
U(64)=[ 32, 16 ]
U(65)=[ 48, 20 ]
U(66)=[ 20, 5 ]
U(67)=[ 66, 4 ]
U(68)=[ 32, 16 ]
U(69)=[ 44, 4 ]
U(70)=[ 24, 9 ]
U(71)=[ 70, 4 ]
U(72)=[ 24, 15 ]
U(73)=[ 72, 2 ]
U(74)=[ 36, 2 ]
U(75)=[ 40, 9 ]
U(76)=[ 36, 5 ]
U(77)=[ 60, 13 ]
U(78)=[ 24, 9 ]
U(79)=[ 78, 6 ]
U(80)=[ 32, 21 ]
U(81)=[ 54, 2 ]
U(82)=[ 40, 2 ]
U(83)=[ 82, 2 ]
U(84)=[ 24, 15 ]
U(85)=[ 64, 26 ]
U(86)=[ 42, 6 ]
U(87)=[ 56, 8 ]
U(88)=[ 40, 14 ]
U(89)=[ 88, 2 ]
U(90)=[ 24, 9 ]
U(91)=[ 72, 36 ]
U(92)=[ 44, 4 ]
U(93)=[ 60, 13 ]
U(94)=[ 46, 2 ]
U(95)=[ 72, 9 ]
U(96)=[ 32, 36 ]
U(97)=[ 96, 2 ]
U(98)=[ 42, 6 ]
U(99)=[ 60, 13 ]
U(100)=[ 40, 9 ]

totient(2)=1
totient(3)=2
totient(4)=2
totient(5)=4
totient(6)=2
totient(7)=6
totient(8)=4
totient(9)=6
totient(10)=4
totient(11)=10
totient(12)=4
totient(13)=12
totient(14)=6
totient(15)=8
totient(16)=8
totient(17)=16
totient(18)=6
totient(19)=18
totient(20)=8
totient(21)=12
totient(22)=10
totient(23)=22
totient(24)=8
totient(25)=20
totient(26)=12
totient(27)=18
totient(28)=12
totient(29)=28
totient(30)=8
totient(31)=30
totient(32)=16
totient(33)=20
totient(34)=16
totient(35)=24
totient(36)=12
totient(37)=36
totient(38)=18
totient(39)=24
totient(40)=16
totient(41)=40
totient(42)=12
totient(43)=42
totient(44)=20
totient(45)=24
totient(46)=22
totient(47)=46
totient(48)=16
totient(49)=42
totient(50)=20
totient(51)=32
totient(52)=24
totient(53)=52
totient(54)=18
totient(55)=40
totient(56)=24
totient(57)=36
totient(58)=28
totient(59)=58
totient(60)=16
totient(61)=60
totient(62)=30
totient(63)=36
totient(64)=32
totient(65)=48
totient(66)=20
totient(67)=66
totient(68)=32
totient(69)=44
totient(70)=24
totient(71)=70
totient(72)=24
totient(73)=72
totient(74)=36
totient(75)=40
totient(76)=36
totient(77)=60
totient(78)=24
totient(79)=78
totient(80)=32
totient(81)=54
totient(82)=40
totient(83)=82
totient(84)=24
totient(85)=64
totient(86)=42
totient(87)=56
totient(88)=40
totient(89)=88
totient(90)=24
totient(91)=72
totient(92)=44
totient(93)=60
totient(94)=46
totient(95)=72
totient(96)=32
totient(97)=96
totient(98)=42
totient(99)=60