Note that is equivalent to . Doesn't this remind you of some algebra´c structure learnt while studying factorization ?
Thanks for the hint but I probably should have asked about equations of the form with p prime as the above hint for this one hasn't helped me.
Factorizing that I can only see two solutions, 1 and 18.
I can't find anything in our notes about this and it's stuck in the middle of a tutorial consisting of primitive root questions so I don't know how to approach it.
I think you already worked out what I'm about to say, but this is just to increase my post count (joking )
So the solutions of are given by :
Solve those for and you will find all the solutions of the congruence. Don't forget to include the four solutions given by the quadratics
What "same result" are you talking about? That they have the same discriminant doesn't mean their roots are the same....
Just apply the well-known formula for the roots of a quadratic equation, which you can do since the characteristic of the field we're working on isn't two.