Solve the congruence.
8x ≡ 1 mod (27)
Thanks!
gcd(8,27)=1 thus there exists a unique congruence class of solutions.
8x = 1 = -26 mod(27)
Thus,
8x = -26 (mod 27)
They share a factor of 2 which is coprime with 27, divide by it.
4x = -13 = 14(mod 27)
Again divide by it,
2x = 7 (mod 27)
Again,
2x = - 20 (mod 27)
x = -10 (mod 27)
Thus,
x = 17 (mod 27)