On the diophantine equation x_1x_2···x_n = h(n)(x_1 + x_2 +...+ x_n) - Bukor, Jozsef; Filakovszky, Péter; Tóth, János T. (Annales Mathematicae Silesianae, 1998)
We are concerned with the equation of the title, where n is a fixed positive integer, h(n) is a given integer-valued arithmetic function and the unknowns take positive integral values 1 ≤ x1 ≤ x2 ≤ ... ≤ xn. We estimate the number m for which xi = 1 (i = 1, 2,...,m) in every solution. Next we give an upper bound for the number of coordinates of a solution which can be greater than 1. Further we estimate the number of all solution of the equation, and the paper concludes with a list of open problems.