The meaning and techniques of mathematical induction are presented on this page:
Bezout's Identity (not Bezout's Theorem) is an important theorem in number theory. It states that if nonzero integers a and b have GCD of d, then there exist integers x and y such that d = ax + by.
The Chinese Remainder Theorem is another important theorem in number theory. The proof is given for only two relatively prime integers.
Chinese Remainder Theorem PDF file
Hyperintegers, being extensions of the integers, are infinite strings of digits with suitable definitions of addition and multiplication to form a ring. This ring has four idempotents, two of which are infinite, nonrepeating sequences of digits.
The Ring of Hyperintegers PDF file This paper gives an introduction to a fascinating extension to the ring of integers, called the 10-adic integers. You can view a presentation on them by the mathematician Richard E. BORCHERDS at p-adic numbers, part 1 of 3.
We wish to characterized how the roots of polynomials depend on their coefficients. Cyclotomic polynomials.
Notes On Vieta's Formulas PDF file
Believing that every quadratic equation has two roots x1 and x2, we can find the values of those roots in terms of the coeffcients of the equation.
Quadratic Roots from Symmetric Polynomials PDF file
This morphism is added to abstract algebra that facilitates proving that a set with a binary operation on it is a group.
Adding a Morphism Theorem to Abstract Algebra PDF file