Re: [問題] 離散 問題
※ 引述《yshihyu (yshihyu)》之銘言：
: X 餘 2 (mod 3)
: X 餘 1 (mod 4)
: X 餘 2 (mod 5)
: 要找X 最小兩個整數值
: 請問最小兩個要怎麼找?
: 答案應該是 17, 77
: 謝謝
利用中國餘數定理
r1 = 2 , r2 = 1 , r3 = 2
n1 = 3 , n2 = 4 , n3 = 5 , n = 60
N1 = 20 , N2 = 15 , N3 = 12
M1 = 20^-1 mod 3 = -1
M2 = 15^-1 mod 4 = -1
M3 = 12^-1 mod 5 = 2
x = r1*M1*N1 + r2*M2*N2 + r3*M3*N3 (mod 60) = 17
x = 17 + 60t (t = 0 ,1)
thus, x = 17 , 77
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