30a-Primes - Primes Introduction Discrete Mathematics...

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Primes Discrete Mathematics
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Discrete Mathematics – Primes 30-2 Previous Lecture Integers Divisor, remainders Properties of divisibility The division algorithm
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Discrete Mathematics – Primes 30-3 Representation of Integers In most case we use decimal representation of integers. For example, 657 means 6 100 + 5 10 + 7 = Let b be a positive integer greater than 1. Then if n is a positive integer, it can be expressed uniquely in the form where k is a nonnegative number, are nonnegative integers less than b, and Such a representation of n is called the base b expansion of n, denoted by
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Discrete Mathematics – Primes 30-4 2 0 2 1 1 2 10 20 0 41 1 2 2 165 2 82 Binary Expansion Important case of a base is 2. The base 2 expansion is called the binary expansion of a number Find the binary expansion of 165 1 165 = 2 82 + 1 2 0 82 = 2 41 + 0 41 = 2 20 + 1 20 = 2 10 + 0 2 0 5 10 = 2 5 + 0 5 = 2 2 + 1 2 = 2 1 + 0 1 = 2 0 + 1
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Discrete Mathematics – Primes 30-5 Hexadecimal Expansion Using A, B, C, D, E, F for 10, 11, 12, 13, 14, 15, respectively, find the base 16 expansion of 175627
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Discrete Mathematics – Primes 30-6 Primes Every integer n (except for 1 and -1) has at least 2 positive divisors, 1 and n (or -n).
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30a-Primes - Primes Introduction Discrete Mathematics...

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