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The linear diophantine problem of Frobenius for subsets of arithmetic sequences

โœ Scribed by Stefan Matthias Ritter

Publisher
Springer
Year
1997
Tongue
English
Weight
216 KB
Volume
69
Category
Article
ISSN
0003-889X

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๐Ÿ“œ SIMILAR VOLUMES

On the Linear Diophantine Problem of Fro
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โœ J.L. Davison ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

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โœ Stefan Matthias Ritter ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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