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Glossary of Number Theory

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


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 k2=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.

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Other glossaries: Geometry Glossary, Statistics Glossary, Topology Glossary

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