Additive

All Numbers Have Prime Divisors

All Numbers have Prime Factorization

Arithmetic Function

Associate

b-ary Representation Theorem

Binary Function (f_b)

Carmichael Number

Characteristic of F

Chinese Remainder Theorem

Composite Number

Congruence

Coprime

Degree is Closed under Addition

Division Algorithm for Polynomials

Division of Polynomials

Equivalence Relation

Euclidean Algorithm

Euler's Criterion

Euler's Theorem

Euler's Totient Function in Terms of Mobius Function

Euler's Totient Function ϕ

Fermat's Little Theorem

Finite Field of Order p

Finite Fields of Same Cardinality = Isomorphic

Finite Subgroups are Cyclic

Fundamental Theorem of Arithmetic

Gauss Sum

Gauss's Formula

Generalized Chinese Remainder Theorem

Generator

Homomorphism

If a Prime divides ab it divides one of a or b

If an Irreducible Polynomial divides ab then it divides a or b

Irreducible (Polynomial)

Irreducible Factorization

Isomorphism

Jacobi Prop 1

Jacobi Prop 2

Jacobi Symbol

Lagrange Corollary

Lagrange Lemma

Lagrange Theorem

lcm Order Lemma

Least Common Multiple

Legendre Prop 3

Legendre Symbol

Legendre Symbol Properties

Lemma 3.1

Lemma 3.2

Min poly. dividing poly. of same root

Minimal Polynomial

Möbius Function

Möbius Inversion Formula

Monic

Multiplicative

Nonzero Constant Polynomials

p-adic Valuation (v_p)

Parity

Perfect Square

Polynomials

Positive Divisor Counter Function (d)

Prime Number

Primitive

Primitive Root

Proper Divisor

Pseudoprime

Pythagorean Triple

Quadratic Reciprocity of Jacobi

Quadratic Reciprocity of Legendre

Quadratic Residue

Relatively Prime

Ring of Polynomials of Order p

Root

Root of Unity

Solution to Congruence

Square of Gauss Sum

Squarefree Number

The Set of Residue Classes mod p

Theorem 1.1

Theorem 1.16

Theorem 1.17

Theorem 1.18

Theorem 1.19

Theorem 1.22

Theorem 1.6

Theorem 3.1

Unique Factorization Theorem for Polynomials

Uniqueness of GCD

Unit

Wilson's Theorem

Writing Primitive Pythagorean Triples