Numerical/Alphabetic Lookup Table
Letter
Value
Letter
Value
A
0
O
14
B
1
P
15
C
2
Q
16
D
3
R
17
E
4
S
18
F
5
T
19
G
6
U
20
H
7
V
21
I
8
W
22
J
9
X
23
K
10
Y
24
L
11
Z
25
M
12
26
N
13
!
27
?
28
Multiplicative Functions
A function is multiplicative if it is true that f (mn) = f (m)f (n) if (m, n) = 1. We define τ (n) as the
number of positive divisors of an integer n (including 1 and n) and σ(n) as the sum of these same positive
divisors. We define φ(n) as the number of integers less than n which are relatively prime to n.
Legendre Symbol Rules:
a
p
!
ab
p
!
1. If a ≡ b (mod p) then
a2
p
2. If p6 | a then
!
=
b
p
!
=
a
p
.
!
= 1.
3. If p6 | a and p6 | b then
b
p
!
.
4. If p and
primes and p ≡ q ≡
! q are odd !
! 3 (mod 4)
! then
p
q
p
q
=−
, otherwise
=
.
q
p
q
p
!
5.
1
p
6.
−1
p
7.
2
p
= 1,
!
(
=
!
(
=
1
−1
1
−1
if p ≡ 1 (mod 4)
if p ≡ 3 (mod 4)
if p ≡ 1, 7 (mod 8)
if p ≡ 3, 5 (mod 8)
Duodecimal Times Tables
5
6
7
8
9
δ
2
δ
10
12
14
16
18
1δ
3
13
16
19
20
23
26
29
4
18
20
24
28
30
34
38
5
21
26
2
34
39
42
47
6
26
30
36
40
46
50
56
7
2
36
41
48
53
5δ
65
8
34
40
48
54
60
68
74
9
39
46
53
60
69
76
83
δ
42
50
5δ
68
76
84
92
47
56
65
74
83
92
δ1
10
50
60
70
80
90
δ0
0
11
55
66
77
88
99
δδ
Small Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97