In my attempt to solve Beal's conjecture I found the exact analytic expression where a prime is the product of a greater prime and a fractional number (screenshot attached).

I used the exact analytic expression in the Beal equation to show that the equation will always have common prime factors and thus the conjecture holds true.

More details about the equations in this research : Article On Beal's Conjecture, the Case (x,y,z)=(n,2n-1,n)

Could you give your opinion ?