Symbol |
Description |
Location |
|
(ring of) integers |
Definition 1.0.1 |
|
counting numbers (starting at zero) |
Definition 1.0.1 |
|
is a divisor of |
Definition 1.2.5 |
|
greatest common divisor of and |
Definition 2.2.1 |
|
greatest integer (floor) function |
Definition 3.3.3 |
|
is congruent to modulo |
Definition 4.1.1 |
|
the equivalence class of modulo some fixed |
Definition 4.4.1 |
|
multiplicative inverse of a number modulo some fixed |
Definition 5.3.4 |
|
product of unspecified, possible identical, primes |
Theorem 6.3.2 |
|
short form for product of primes |
Example 6.3.3 |
|
alternate short form for product of primes |
Example 6.3.3 |
|
product of unspecified distinct prime power |
Example 6.3.4 |
|
short form for product of prime powers |
Example 6.3.4 |
|
for prime, but does not divide |
Definition 6.4.5 |
|
factorial |
Definition 6.4.6 |
|
(ring of) integers modulo |
Definition 8.1.1 |
|
the set of all elements in except |
Example 8.3.4 |
|
order of a group |
Definition 8.3.8 |
|
order of a group element |
Definition 8.3.10 |
|
group of units modulo |
Definition 9.1.2 |
|
order of the group of units of (Euler function) |
Definition 9.2.1 |
|
alternate notation for Euler function |
Definition 9.2.1 |
|
Fermat number |
Definition 12.1.1 |
|
Mersenne number |
Definition 12.1.6 |
|
number of different ways to write as a sum of two squares |
Exercise 13.7.7 |
|
Gaussian integers |
Definition 14.1.2 |
|
complex numbers |
Definition 14.1.2 |
|
number of different ways to write as a sum of perfect squares |
Example 14.2.3 |
|
abbreviation for ‘quadratic residue’ |
Definition 16.3.1 |
|
group of quadratic residues of |
Definition 16.4.2 |
|
Legendre symbol, for an odd prime |
Definition 16.6.1 |
|
multiples of positive even numbers less than by |
Definition 17.2.2 |
|
set of nonnegative remainders of elements of modulo |
Definition 17.2.2 |
|
remainder modulo of the element of |
Definition 17.2.2 |
|
Jacobi symbol, odd |
Definition 17.4.9 |
|
sum in proof of quadratic reciprocity |
Paragraph |
|
sum in proof of quadratic reciprocity |
Paragraph |
|
alternate notation for |
Definition 18.2.1 |
|
sum of th powers of divisors of |
Definition 19.1.1 |
|
number of (positive) divisors of |
Remark 19.1.2 |
|
sum of (positive) divisors of |
Remark 19.1.2 |
|
unit function |
Definition 19.2.9 |
|
identity function |
Definition 19.2.9 |
|
abundancy index of |
Fact 19.4.9 |
|
‘Big Oh’ notation that a function is less in absolute value than for some constant |
Definition 20.1.2 |
|
natural (base ) logarithm |
Definition 20.3.3 |
|
Euler-Mascheroni gamma constant, limit of difference between the harmonic series and natural logarithm |
Definition 20.3.10 |
|
Gamma function factorial extension |
Remark 20.3.11 |
|
prime counting function |
Definition 21.0.1 |
|
number of integers coprime to first primes |
Definition 21.1.7 |
|
the th prime |
Definition 21.1.7 |
|
logarithmic integral |
Definition 21.2.2 |
|
Chebyshev theta function |
Definition 21.4.3 |
|
prime number indicator function |
Definition 21.4.7 |
|
primorial (product of primes up to ) |
Definition 22.2.7 |
|
twin prime constant |
Remark 22.3.6 |
|
Moebius function of |
Definition 23.1.1 |
|
Dirichlet product of and as arithmetic functions |
Definition 23.2.3 |
|
Dirichlet product identity function |
Definition 23.3.1 |
|
number of unique prime divisors of |
Definition 23.3.3 |
|
alternate notation for |
Definition 23.3.3 |
|
Liouville's function |
Definition 23.3.4 |
|
Riemann zeta function |
Definition 24.2.1 |
|
auxiliary function in Riemann explicit formula |
Definition 25.4.2 |