Linear Diophantine Problems

Mehdi Djawadi and Gerd Hofmeister
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Gerd Hofmeister: Johannes Gutenberg-Universität, Fachbereich 17 (Mathematik)

Chapter 6 in Number Theory: New York Seminar 1991–1995, 1996, pp 91-95 from Springer

Abstract: Abstract The Frobenius number g(A k ) Let A k $${A_k} = \{ {a_1},...,{a_k}\}\subset$$ IN with gcd(A k ) = 1, n $$ \in I{N_0}.$$ If (1) $$n = \sum\limits_{i = 1}^k {{x_i}{a_i},{x_i}}\in I{N_0}$$ we call this a representation or a g-representation of n by Ak (in order to distinguish between several types of representations that will be considered in the sequel). Then the Frobenius number g(A k ) is the greatest integer with no g-representation.

Date: 1996
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DOI: 10.1007/978-1-4612-2418-1_6

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