On the diophantine equation x_1x_2···x_n = h(n)(x_1 + x_2 +...+ x_n)

Jozsef Bukor; Péter Filakovszky; János T. Tóth

Published: 1998-09-30

Vol. 12 (1998)

On the diophantine equation x_1x_2···x_n = h(n)(x_1 + x_2 +...+ x_n)

Jozsef Bukor , Péter Filakovszky , János T. Tóth

Abstract

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 ≤ ... ≤ x_n. We estimate the number m for which x_i = 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.

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Bukor, J., Filakovszky, P., & Tóth, J. T. (1998). On the diophantine equation x_1x_2···x_n = h(n)(x_1 + x_2 +.+ x_n). Annales Mathematicae Silesianae, 12, 123–130. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14169

Jozsef Bukor

jbukor@ukf.sk

Affiliation:

Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University, Slovakia Slovakia

Péter Filakovszky

Affiliation:

Nové Zámky, Slovakia Slovakia

János T. Tóth

Affiliation:

Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University, Slovakia Slovakia

Vol. 12 (1998)
Published: 1998-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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