Reciprocity Theorem
If there exists a Rational Integer 
such that, when 
, 
, and 
are Positive Integers,
then
is the -adic reside of , i.e., is an -adic residue of Iff 
is solvablefor . Reciprocity theorems relate statements of the form `` is an -adic residue of '' with reciprocal statements ofthe form `` is an -adic residue of .''The first case to be considered was 
(the Gauß 
gave the firstcorrect proof. Gauss also solved the case 
(Cubic Reciprocity Theorem) using Integers of theform 
, where 
is a root of 
and 
, 
are rational Gauß stated the case 
(Quartic Reciprocity Theorem) using the Gaussian Integers.
Proof of -adic reciprocity for Prime was given by Eisenstein in 1844-50 and by Kummer in 1850-61. Inthe 1920s, Artin formulated Artin's Reciprocity Theorem, a general reciprocity law for all orders.
- Hall-Janko Group
- Halphen Constant
- Halphen's Transformation
- Halting Problem
- Hamiltonian Circuit
- Hamiltonian Cycle
- Hamiltonian Graph
- Hamiltonian Group
- Hamiltonian Map
- Hamiltonian Path
- Hamiltonian System
- Hamilton's Equations
- Hamilton's Rules
- Hammer-Aitoff Equal-Area Projection
- Hamming Function
- Ham Sandwich Theorem
- Handedness
- Handkerchief Surface
- Handle
- Handlebody
- Hankel Function
- Hankel Function of the First Kind
- Hankel Function of the Second Kind
- Hankel Matrix
- Hankel's Integral