Greatest Common Divisors, Diophantine Equations, and Combinatorics

Richard S Millman,Peter J Shiue,Eric Brendan Kahn

doi:10.1007/978-3-319-14427-6_2

Greatest Common Divisors, Diophantine Equations, and Combinatorics

Richard S Millman, Peter J Shiue + Show 1 more

https://doi.org/10.1007/978-3-319-14427-6_2

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Publication Date: Jan 1, 2015

Affiliation: University of Nevada, Las Vegas, Bloomsburg University, Georgia Institute of Technology

#Fundamental Theorem Of Arithmetic #Diophantine Equations + Show 8 more

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Abstract

Introduction This chapter deals with the structure of how prime numbers are put together (Prime Factorization) and the tools of number theory which include greatest common divisors (GCD), least common multiples (LCM). These tools provide the beginning of important theorems such as the Fundamental Theorem of Arithmetic and the Euclidean Algorithm and its byproduct. Problems which have only solutions in integers (Diophantine equations) are discussed. Application to combinatorics is also mentioned.

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