During the early part of the last century, Ferdinand Georg Frobenius
(1849–1917) raised, in his lectures. At first glance, FP may look deceptively specialized. Nevertheless
it crops up again and again in the most unexpected places. It turned
out that the knowledge of g(a1,...,an) has been extremely useful to
investigate many different problems. A number of methods, from several areas of mathematics, have been
used in the hope of finding a formula giving the Frobenius number
and algorithms to calculate it. The main intention of this book is
to highlight such ‘methods, ideas, viewpoints and applications’ for as
wide an audience as possible. The results on FP are quite scattered
in the literature and, at present, there is no complete or accessible
source summarizing the progress on it. This book aims to provide a
comprehensive exposition of what is known today on FP.