Interesting Math History

Question :
What is the 'Theory of Numbers' ?

Answer :
The Theory of Numbers is concerned with the study of the properties of integers or whole numbers. The proofs of many of the Theory use the deepest resources of mathematics. However, some of the most interesting conjectures are still unproved.
Topics of the Theory of the Numbers can be listed as follows :
I. Divisibility and Primality :
   a. Elementary Definitions; Factorization into Primes.
   b. Residue Classes; Eulers Theorem
   c. Congruences in one unknown
   d. Quadratic Residues; The Quadratic Reciprocity Law
   e. Factorization of Numbers; Mersenne Primes

II. Representation by forms :
    a. Binary Quadratic forms
    b. Genera of Quadratic forms; Formulas for Number of Representations
    c. The Numbers represented by a Quadratic Form : universal forms Representation of zero.
    d. Automorphs and Reduction of indefinite Binary Quadratic Forms
    e. Diophantine Equations

III. Topics in Analytic Number Theory :
     a. Gauss's Class-Number Conjencture
     b. Distribution of Primes; Asymptotic Formulas

IV. Additive Theory of Numbers :
     a. Partitions
     b. The waring problem and related problems
     c. The Goldbach Problem

V. Diophontine Approximation :
    a. Geometry of Numbers
    b. Diophontine Approximation

VI. Generalisations of Arithmetic :
     a. Algebraic Numbers
     b. Ideals
     c. Algebras and their Arithmetics