On a property of the division algorithm and its application to the theory of non-unique factorizations (Q1045951)

For \(1<a<n\) write \(n=qa+r\) with \(0\leq r<n\) and put \(\sigma_{n,a}=q+r\). The authors show that for \(n\geq3\) this function takes all integer values in the interval \([2,(n+1)/2]\) and determines the cases when it assumes the maximal value.