Exponential diophantine problems

(ap-1 – 1)/pk with arbitrary k Abstract: Fermat quotients with arbitrary k are considered on an introduc-tory level. While the ongoing research on fermat-quotients is concerned with the very difficult problem to find an appropriate primenumber p for k>1 and a given base a, the article here is primarily concerned with the much simpler problem of finding appropriate bases a if the primenumber p is given. In chapter 3 I do a first step into the more difficult problem of finding primes for given small bases. I begin generalizing the problem to compos-ite n instead of prime p, making it an "Euler-quotient " to get more heuris