ON THE NUMBER OF SOLUTIONS FOR THE EQUATION
For every positive integer m, we consider the equation We prove that is the only case in which the above equation admits infinitely many solutions. We point out several cases in which the equation has no solutions. We also show that there exist such equations, for which the number of solutions is greater than a given natural number. At the end, we point out some open questions.
Euler?s totient, equation, number of solutions.
