Question

please help me in solving this
57^x≡2 (mod 23)

Answer 1

1st since 5 is primitive root of 23
so find indices
5≡5
5^2≡2
5^3≡10
5^4≡4
5^5≡20
5^6≡8
5^7≡17
5^8≡16
5^9≡ 11

Answer 2

mod 23

Answer 3

5^9≡ 11≡ 57

Answer 4

now
57^x≡ 2 mod 23
x index 57≡ index 2 mod 22
9x≡ 2 mod 22
9x≡ 90 mod 22
x≡ 10 mod 22

Answer 5

now how can i convert it into mod 23???

Answer 6

and please tell me i m doing right or wrong???