List of Symbols
Symbol Meaning Page
Z set of integers (3)
x ∈Sxbelongs to set S (3)
x /∈Sxdoes not belong to set S (3)
Z
+
set of positive integers (3)
N set of positive integers (3)
W set of whole numbers (4)
a < bais less than b (4)
a > bais greater than b (4)
a ≤ba< b or a =b (5)
a ≥ba> b or a =b (5)
min{x, y} the minimum of x and y (5)
max{x, y} the maximum of x and y (5)
|x| the absolute value of x (5)
x the floor of the real number x (6)
x the ceiling of the real number x (6)
i=m
i=k
a
i
=
m
i=k
a
i
=
m
k
a
i
a
k
+a
k+1
+···+a
m
(9)
i∈I
a
i
the sum of the values of a
i
as i runs over the various values in I (11)
P
a
ij
the sum of the values of a
ij
, where i and j satisfy properties P (11)
i=m
i=k
a
i
=
m
i=k
a
i
=
m
k
a
i
a
k
a
k+1
···a
m
(13)
n! n factorial (13)
n
r
binomial coefficient (33)
t
n
triangular number (40)
s
n
square number (44)
p
n
pentagonal number (46)
h
n
hexagonal number (48)
T
n
tetrahedral number (49)
S
n
square pyramidal number (50)
P
n
pentagonal pyramidal number (51)
H
n
hexagonal pyramidal number (51)
a div b the quotient when a is divided by b (71)
a mod b the remainder when a is divided by b (71)
Symbol Meaning Page
a|bais a factor of b (74)
a bais not a factor of b (74)
|A| the number of elements in set A (76)
A ∪B the union of sets A and B (76)
A ∩B the intersection of sets A and B (76)
A
the complement of set A (76)
N =(a
k
a
k−1
...a
1
a
0
)
b
base-b representation of N (83)
R
n
repunit with n ones (96)
π(x) the number of primes ≤x (110)
F
n
the nth Fibonacci number (129)
L
n
the nth Lucas number (136)
|A| the determinant of matrix A (138)
f
n
the nth Fermat number (139)
(a, b) the greatest common factor of a and b (155)
(a
1
, a
2
,...,a
n
) the greatest common factor of a
1
, a
2
,..., and a
n
(162)
p
a
np
a
exactly divides n (183)
[a, b] the least common multiple of a and b (184)
[a
1
, a
2
,...,a
n
] the least common multiple of a
1
, a
2
,..., and a
n
(187)
a ≡b (mod m) a is congruent to b modulo m (212)
a ≡b (mod m) a is not congruent to b modulo m (212)
[r] the congruence class represented by r (216)
a
−1
an inverse of a modulo m (234)
ρ(n) the digital root of n (291)
I
n
the identity matrix of order n (316)
n# the product of primes ≤n (325)
ϕ(n) Euler’s phi function (342)
τ(n) the number of positive factors of n (365)
σ(n) the sum of the positive factors of n (366)
M
p
Mersenne number 2
p
−1 (381)
μ(n) Möbius function (398)
λ(n) Liouville function (405)
ord
m
a the order of a modulo m (456)
ψ(d) the number of incongruent residues of order d modulo p (470)
ind
α
a theindexofa to the base α (483)
(a/p) Legendre symbol (501)
(a/m) Jacobi symbol (527)
(a/n) Kronecker symbol (549)
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