What is the likely amount of solutions to the problem xt = a in the field F*p and does is this determined by a? Given that p is a prime number, t is any divisor of p-1, and an a that is an element in the field F*p.    I know the best way to solve this problem is by first setting a value r that is a primitive root (r (mod p)) and then taking the logr of x and a. Which can then let the original equation become t (logr(x)) ≡ (logr(a)) (mod p − 1) which will help calculate the possible amount of solutions for the new equation. I need someone to explicitly label the steps for me.

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