I have been given a question which is

Write down a table of indices to the base 3 modulo 17. Use this to find all the solutions of the congruence

3x^5 = 1 (mod 17)

I've managed to do the table of indices and that's correct but my answer for the solution is x = 5 (mod17) and it says that the answer is x = 10 (mod17). and i dont know where im going wrong?

any help is much appreciated if you can get to the right answer?

Thanks very much