# Modular Arithmetic

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## Abstract

Modular arithmetic is a way of studying divisibility properties of natural numbers. It provides techniques for easily answering questions such as whether 3 plus 2 to the power 3,000,005 is divisible by 7. It has a number of applications, such as proving that a natural number is divisible by 9 if and only if the sum of its digits is divisible by 9. More importantly, it includes theorems such as Fermat’s (see Chapter 5) which are useful in many contexts, including in developing a technique for sending secret messages (see Chapter 6).

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