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1.9y²:

XJP´ƒê,a´󰀂ê§@o7½kp󰀁a,,󰀂dEuler½nŒ•§aϕ(m)≡1(modm),m•ƒê,duP´ƒê§ϕ(p)=p−1¤±ap−1≡1(modp)Kap−1−1≡0(modp)@op|ap−1−11.10y²µ

(⇐)dŸê󰀂󰀄Ó{ª§éu?Û󰀂êx5`§p•ƒê§k±e½n¤áxp−1≡(x−1)(x−2)···(x−(p−1))(modp)󰀂x=0ž§=󰀃

(⇒)(‡y)b󰀂p´Üê§K∃a,b∈Z,0a|[(p−1)!+1]⇒a|1=[(p−1)!+1]−(p−1)!⇒a=1gñ§ddŒ•p•ƒê1.11y²

XJp´ƒê§dWilson½nŒ•

(p−j)!=(p−1)(p−2)···(p−j)(p−j−1)!≡(−1)(−2)···(−j)(p−j−1)!≡(−1)j∗j!(p−1−j)!(modp)

p−1)!j

⇒j!((p−j−1)!≡(−1)(modp)

jj⇒Cp−1≡(−1)(modp)1.13y²

,i=1,2,···,k,KPMi=mi

x≡

󰀁

k󰀁i=1

MiMiai(modm)(󰀅)

󰀁

w,´Ó{ª|󰀄),Ù¥MiMi≡1(modmi),i=1,2,···,k.

ey•˜5µ

ex1≡x2´·ÜÓ{ª|󰀄?¿ü‡󰀂ê,Kx1≡x2(modmi),i=1,2,···,k,

Ï(mi,mj)=1,u´x1≡x2(modm),󰀂Ó{ª|󰀄)•k(󰀅)

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