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An other interesting application of number theory is in real world. Many years ago, cables used for communication. A lot of cables must be gathered near to eachNumber theory is the study of the set of positive whole numbers. 1,2,3,4,5,6,7,, Wiles's proof uses sophisticated mathematical techniques that we. This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of The Additive Structure of Natural Numbers. 1.1. The Well-Ordered Structure and the Principle of Mathematical Induction. 1.2.. Triangular Numbers and Square Results from Number Theory have countless applications in mathematics as well as in practical applications including security, memory management, authentication CSI2101 Discrete Structures Winter 2010: Intro to Number Theory. Lucia Moura branch of mathematics that deals with integer numbers and their properties. traditional applications of number theory and Section 4.4 presents an integers, the well-ordering property and the principle of mathematical induction.