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The Diophantine Frobenius Problem


During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he 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 FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating 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 to a broader aud Hide synopsis

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