The Diophantine Frobenius Problem

During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the following problem, known as the 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 nonnegative integer combination of a1,,an.
At first glance FB may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been…