During the early part of the last century, Ferdinand Georg Frobenius
(1849–1917) raised, in his lectures (according to [57]), the following
problem (called the diophantine Frobenius Problem FP): given relatively
prime positive integers a1,...,an, find the largest natural number
(called the Frobenius number and denoted by g(a1,...,an)) that is not
representable as a non-negative integer combination of a1,...,an.
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