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27 Functions of Number TheoryNotation

§27.1 Special Notation

(For other notation see Notation for the Special Functions.)

d,k,m,n

positive integers (unless otherwise indicated).

d|n

d divides n.

(m,n)

greatest common divisor of m,n. If (m,n)=1, m and n are called relatively prime, or coprime.

(d1,,dn)

greatest common divisor of d1,,dn.

d|n, d|n

sum, product taken over divisors of n.

(m,n)=1

sum taken over m, 1mn and m relatively prime to n.

p,p1,p2,

prime numbers (or primes): integers (>1) with only two positive integer divisors, 1 and the number itself.

p, p

sum, product extended over all primes.

x,y

real numbers.

nx

n=1x.

ζ(s)

Riemann zeta function; see §25.2(i).

(n|P)

Jacobi symbol; see §27.9.

(n|p)

Legendre symbol; see §27.9.