# Number theory is the study of the set of positive whole numbers 1,2,3,4,5,6,7,…,which are often called the set of natural numbers. We will especially want to study the relationships between

Number theory is the study of the set of positive whole numbers 1,2,3,4,5,6,7,…,which are often called the set of natural numbers. We will especially want to study the relationships between different sorts of numbers. Since ancient times, people have separated the natural numbers into a variety of different types. Here are some familiar and not-so-familiar examples: odd 1,3,5,7,9,11,… even 2,4,6,8,10,… square 1,4,9,16,25,36,… cube 1,8,27,64,125,… prime 2,3,5,7,11,13,17,19,23,29,31,… composite 4,6,8,9,10,12,14,15,16,… 1 (modulo 4) 1,5,9,13,17,21,25,… 3 (modulo 4) 3,7,11,15,19,23,27,… triangular 1,3,6,10,15,21,… perfect 6,28,496,… Fibonacci 1,1,2,3,5,8,13,21,… Learn more by looking at Chapter 2 It is important to understand Number Theory to understand Encryption particularly Asymmetrical Encryption. states that if is a , then for any , the number − is an integer multiple of . In the notation of , this is expressed as: For example, if = 2 and = 7, then 27 = 128, and 128 − 2 = 126 = 7 × 18 is an integer multiple of 7. If is not divisible by , Fermat’s little theorem is equivalent to the statement that − 1 − 1 is an integer multiple of , or in symbols: For example, if = 2 and = 7, then 26 = 64, and 64 − 1 = 63 = 7 × 9 is thus a multiple of 7

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