掌握的知識點：

• Prime Numbers
• Fermat's and Euler's Theorems?
• Testing for Primality
• The Chinese Remainder Theorem
• Discrete Logarithms

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?Prime Numbers

Prime numbers only have divisors of 1 and self

• cannot be written as a product of other numbers
• 1 is prime,but is generally not of interest

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Prime numbers are central to number theory!

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List of prime number less than 200 is:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199

上面看出素數(shù)一定是奇數(shù)(except 2)，如果是偶數(shù)肯定不是素數(shù)

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Prime? factorisation of a number n is when its written as a product of primes:?

其中，P是所有素數(shù)的集合，a是任意正整數(shù)

比如， 91=7* 13,? 3600= 2^4 *? 3^2 * 5^2

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兩個數(shù)互素的條件：

Two numbers a, b are relatively prime if have no common divisors other than 1.

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Conversely can determine the greatest common divisor by comparing their prime factorizations and using least powers.

example: 300=2^1 * 3^1 * 5^2 ,? ?18= 2^1 * 3^2?

thus gcd(18,300)=2^1 * 3^1 *5^0= 6

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