On a linear diophantine problem for geometrical type sequences
Let \(A=\{a_ 0,a_ 1,...,a_ n\}\) be a set of relatively prime positive integers, g(A) the Frobenius number, i.e. the greatest b for which \(b=\sum^{n}_{i=0}a_ ix_ i\) has no solution in nonnegative integers \(x_ i\), and n(A) the number of all positive b for which there is no such solution. In this paper the author gives the exact values of g(A) and n(A) in the case where the set A forms an almost geometric progression \(a_ j=h_ ja_ 0+\prod^{j-1}_{i=0}q_ i\) for \(j=1,...,n\), \(g.c.d.(a_ 0,q_ 0)=0\) with \(a_ 0\), \(h_ j\), \(q_{j-1}\), \(j=1,...,n\) given positive integers.
scientific article; zbMATH DE number 3995770