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The Diophantine Frobenius problem

✍ Scribed by Jorge L. Ramírez Alfonsín

Book ID
127425960
Publisher
Oxford University Press
Year
2005
Tongue
English
Weight
1 MB
Series
Oxford lectures series in mathematics and its applications 30
Category
Library
City
Oxford; New York
ISBN
0198568207

No coin nor oath required. For personal study only.

✦ Synopsis

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 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.

📜 SIMILAR VOLUMES

The diophantine Frobenius problem
The diophantine Frobenius problem
✍ Jorge L. Ramírez Alfonsín 📂 Library 📅 2005 🏛 Oxford University Press 🌐 English ⚖ 4 MB

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 repre

On the Linear Diophantine Problem of Fro
On the Linear Diophantine Problem of Frobenius
✍ J.L. Davison 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 351 KB

Suppose \(a, b, c\) are three positive integers with \(\mathrm{gcd}=1\). We consider the function \(f(a, b, c)\) defined to be the largest integer not representable as a positive integral linear combination of \(a, b, c\). We give a new lower bound for \(f(a, b, c)\) which is shown to be tight, and

On a Linear Diophantine Problem of Frobe
On a Linear Diophantine Problem of Frobenius: Extending the Basis
✍ Stefan Matthias Ritter 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 233 KB

Let X k =[a 1 , a 2 , ..., a k ], k>1, be a subset of N such that gcd(X k )=1. We shall say that a natural number n is dependent (on X k ) if there are nonnegative integers x i such that n has a representation n= k i=1 x i a i , else independent. The Frobenius number g(X k ) of X k is the greatest i