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buzzmath
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Can anyone help me with this problem?
Find all solutions of the following congruence 3x^5≡1(mod 23)
This is what I have so far
I know 5 is a primitive root and I made a table of indices modulo 23 with respect to 5
then
Φ(23)=22
Ind5(3x5)≡ind5(1)=22(mod 22)
Ind5(3x5)≡ind5(3) + ind5(x5)≡16 + 5ind5(x)(mod22)
16+5ind5(x)≡22(mod22)
5ind5(x)≡6(mod22)
I'm stuck here because I'm not really sure how to get rid of the 5 on the left side or if I even have to.
Thanks
Find all solutions of the following congruence 3x^5≡1(mod 23)
This is what I have so far
I know 5 is a primitive root and I made a table of indices modulo 23 with respect to 5
then
Φ(23)=22
Ind5(3x5)≡ind5(1)=22(mod 22)
Ind5(3x5)≡ind5(3) + ind5(x5)≡16 + 5ind5(x)(mod22)
16+5ind5(x)≡22(mod22)
5ind5(x)≡6(mod22)
I'm stuck here because I'm not really sure how to get rid of the 5 on the left side or if I even have to.
Thanks
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