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Extending The Linear Diophantine Problem

Marketed By :  LAP LAMBERT Academic Publishing   Sold By :  Kamal Books International
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• Product Description

Given integer-valued relatively prime `coins' a1; a2; :::; ak, the Frobenius number is the largest integer n such that the linear diophantine equation a1m1 + a2m2 + ::: + akmk = n has no solution in non-negative integers m1;m2; :::;mk. We denote by g(a1; :::; ak) the largest integer value not attainable by this coin system. That is to say that any integer x greater than the Frobenius number g(a1; :::; ak) has a representation x = a1x1 + a2x2 + ::: + akxk by a1; a2; :::; ak for some non-negative integers x1; x2; :::; xk. We say x is representable by a1; a2; :::; ak. While it is obvious that there are representable positive integers and non-representable positive integers, must there be a largest non-representable integer? Maybe there are indefinitely large non-representable integers for a1; a2; :::; ak with gcd (a1; a2; :::; ak) = 1. This notion of whether or not the Frobenius number is well-defined will be the first bit of mathematics we look at in this paper. Proposition 1.1. The Frobenius number g(a1; :::; ak) is well-defined. Proof. Given a1; a2; :::; ak with gcd (a1; a2; :::; ak) = 1, the extended Euclidean algorithm gives that there exist m1;m2; :::;mk 2 Z such that...

Product Specifications
 SKU : COC93647 Author Curtis Kifer Language English Binding Paperback Number of Pages 64 Publishing Year 2011-09-28T00:00:00.000 ISBN 978-3845405131 Edition 1 st Book Type Mathematics Country of Manufacture India Product Brand LAP LAMBERT Academic Publishing Product Packaging Info Box In The Box 1 Piece Product First Available On ClickOnCare.com 2015-08-14 00:00:00
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