Quantum integers and cyclotomy (Q1764782)

As main result the authors offer the general rational function solutions with rational coefficients \(\mathcal{F}=\{f_n\}\) of the sequence of functional equations \(f_{mn}(q)=f_m(q)f_n(q^m)\;(m,n\in\mathbb{N})\) if there exists a set \(P\) of at least two prime numbers such that the set \(S(P)\) of all positive integers that are products of powers of prime numbers in \(P\) equals \(\{\ell\in \mathbb{N} : f_\ell\neq 0,\;f_\ell\in \mathcal{F}\}.\) See also the corrigendum [ibid. 145, 632--634 (2014; Zbl 1296.11010)].