The Diophantine Frobenius Problem
The Diophantine Frobenius Problem by Jorge L. Ramírez Alfonsín, published by OUP Oxford in December 2005, is a comprehensive exploration of a significant mathematical challenge posed by Ferdinand Georg Frobenius. This edition spans 243 pages and is presented in English. The book delves into the Frobenius Problem, which involves determining the largest natural number that cannot be expressed as a nonnegative integer combination of given relatively prime positive integers. While the problem may initially seem specialized, it has proven to be relevant across various mathematical contexts.
Readers will find a detailed examination of the methods and ideas surrounding the Frobenius number, as well as its applications in number theory and mathematics at large. The author aims to make these concepts accessible to a broader audience, illustrating how the Frobenius Problem appears in unexpected areas and contributes to the investigation of diverse mathematical issues. This work serves as a valuable resource for those interested in the intersections of mathematics and number theory.
Official synopsis Publisher
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 audience.
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