掌握的知识点：
- Prime Numbers
- Fermat's and Euler's Theorems
- Testing for Primality
- The Chinese Remainder Theorem
- Discrete Logarithms
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
Prime numbers are central to number theory!
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
上面看出素数一定是奇数(except 2)，如果是偶数肯定不是素数
Prime factorisation of a number n is when its written as a product of primes:
其中，P是所有素数的集合，a是任意正整数
比如， 91=7* 13, 3600= 2^4 * 3^2 * 5^2
两个数互素的条件：
Two numbers a, b are relatively prime if have no common divisors other than 1.
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