Number theory: an applied approach/ Rowan Payne ed.

Includes bibliography and index

Complementary families of the Fibonacci-Lucas relations -- Invariant measures for new classes of piecewise fractional linear maps -- Determinantal expressions for Bernoulli polynomials -- Polychromatic colorings on the integers -- Some explicit formulas for Euler-Genocchi polynomials -- On generalized derangements and some orthogonal polynomials -- Additive volume of sets contained in few arithmetic progressions -- Minimum coprime labelings for operations on graphs -- The Unit structure in a quotient ring of a quadratic number field -- On algorithms to calculate integer complexity -- Triangular Ramsey numbers -- An alternative proof of Melham's identities

Number theory is a branch of pure mathematics that deals with the study of natural numbers and integers. It focuses on the set of positive whole numbers which are called the set of natural numbers. The number theory helps in discovering interesting relationships between different sorts of numbers and in proving their legitimacy. It includes both experimental and theoretical aspects. The experimental aspect generates new questions and discovers their answer. The theoretical aspect tries to devise an argument that provides a conclusive answer to the questions. This book covers in detail some existent theories and innovative concepts revolving around number theory. Most of the topics introduced herein cover new techniques and applications of number theory. This book is appropriate for students seeking detailed information in this area as well as for experts.