In this paper on the “Brocard’s Problem” , I have worked on case when n is prime and n divides m-1. Necessary conditions on m are given in Theorem and Corollaries.
I used necessary and sufficient condition of primes. Assuming that n is prime and divides m-1, I applied Inverse Laplace Transform on the obtained equation and got a polynomial function which is easier to deal with. I worked with zero of the polynomial function and got lower bound of p which was not useful as p tends to infinity, but solving quartic equation which I have given at the end could give significant upper, lower bounds of p.
What would happen to those upper, lower bounds if p tends to infinity?