### Glossary of Number Theory

Terms used in number theory, the branch of mathematics concerned with
properties of the integers.

### Glossary

**Jacobi symbol** - (a/p), where p is an odd prime, and a is an integer.
If GCD(a,p)≠1 then (a/p)=0. Otherwise, (a/p)=1 if a is a quadratic
residue (mod p), and (a/p)=-1 if a is a quadratic non-residue (mod p).

**pairwise coprime** - a set of integers is pairwise coprime if no two
elements of the set share any factor other than 1 or -1. (Note: 1 is
coprime to every integer by this definition.)

**quadratic residue** - a square, modulo some number. A number, n,
is said to be a quadratic residue (mod p) if k^{2}=n (mod p) for some
integer, k.

**quadratic non-residue** - a non-square, modulo some number. If n
is not a quadratic residue (mod p), then n is a quadratic non-residue (mod p).
It's a bit of an odd expression, since a residue (mod p) of a number, n, is the
remainder upon division of n by p. If it happens that n isn't the square
of any number, that doesn't make n a non-residue, but perhaps non-quadratic.

### Related pages in this website

Other glossaries: Geometry Glossary,
Statistics Glossary,
Topology Glossary

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Graeme McRae.