caa a22 4500 605508658 CHVBK 20210128100637.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00010-014-0302-6 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0302-6 Bašić Bojan Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia aut On a functional equation related to roots of translations of positive integers [Elektronische Daten] [Bojan Bašić] We consider the functional equation f q (n) =f(n +1) +k, where $${q \geqslant 2}$$ q ⩾ 2 and $${k \in \mathbb{Z}}$$ k ∈ Z are given, and $${f :\mathbb{N} \to \mathbb{N}}$$ f : N → N . This functional equation is related to roots of translations of positive integers, and another motivation for studying this functional equation is the fact that it can be thought of as the "prototypical case” of a more general functional equation of a very broad scope. Our main result is that the considered functional equation has a solution if and only if either k =0 or $${k \geqslant -1}$$ k ⩾ - 1 and $${q - 1\mid k + 1}$$ q - 1 ∣ k + 1 . We further find all solutions for the case q = 3 and k = 1, which is an example that illustrates that the considered functional equation can have a very unexpected set of solutions even with quite small parameters. Springer Basel, 2014 Functional equation nationallicence iterative root nationallicence translation nationallicence Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1195-1205 0001-9054 89:4<1195 2015 89 10 https://doi.org/10.1007/s00010-014-0302-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0302-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bašić Bojan Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1195-1205 0001-9054 89:4<1195 2015 89 10