ΥڡϤƤʥ֥åޡɲΥڡޤϤƤʥ֥åޡ Υڡlivedoor åפɲΥڡޤlivedoor å

ܼ

Fp-2βˡ

ʲμFp-2򤯤ȤǤ롣

1xn=aͿ롣

2Fpˤϸr1֡

3rȤaؿǤIndr(a)׻ơiȤ

i:=Indr(a)

4X=Indr(a)Ȥ

5(n,p-1)=d롣

6diǤ뤫ݤˤäƾʬ롣

[1]diǤʤʤСϤʤ

[2]diǤʤС1ƱnXi (mod p-1)βˡ¹ԤβX1,,XdȤ롣

7x=r^{x_1},~\cdots,~r^{x_d}뺬Ǥ롣

[]F7ˤx4=2򤯡

1ޤϸȤơ3Ǥ

ʤ3ϸǤ뤳ȤʲdzΤƤ

  • 31=3
  • 32=92 (mod 7)
  • 33=6
  • 34=184 (mod 7)
  • 35=125 (mod 7)
  • 36=151 (mod 7)

6(=7-1)褷ƽơˡ71Ȱפ뤿ᡢ3ϸϸǤ롣

2

x^4~=~2
Ind_3(x^4)~=~Ind_3(2)ʢξդФơ3Ȥؿ
Ind_3(x^4)~=~2ʢؿꡢդ׻롣3^\alpha~\equiv~2~\,~\pmod{7}

3d=(n,p-1)=(4,7-1)=(4,6)=2Ǥꡢd=2i=Ind_3(x^4)~=~2Ǥ롣

4ǡX=ind3(x)Ȥȡˡ6(=7-1)˴ؤƱ4X~\equiv~2~\,~\pmod{6}

4X~\equiv~2~\,~\pmod{6}
X~\equiv~2,5~\,~\pmod{6}

äơFpˤơx=32,35¨x=2,5٤ƤκǤ롣