Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 246.10010
Autor: Erdös, Paul; Graham, Ronald L.
Title: On a linear diophantine problem of Frobenius. (In English)
Source: Acta Arith. 21, 399-408 (1972).
Review: Let a1, ... ,an be a sequence of integers satisfying (a1, ... ,an) = 1. Denote by G(a1, ... ,an) the greatest integer N for which N = sum ni = 1ciai, ci \geq 0 integer, has no solution. The problem of determining or estimating G(a1, ... ,an) is due to Frobenius and the problem has a large literature. The authors prove among others G(a1, ... ,an) \leq 2an-1 [{an \over n} ] -an. Put g(n,t) = maxai G(a1, ..., an) where the maximum is taken over all the ai satisfying 0 < a1 < ... < an \leq t, (a1, ... ,an) = 1. Several results are proved about g(n,t) and some open problems are stated one of which has been settled in a recent paper of M. Lewin [cf. the preceding review, J. Lond. Math. Soc., II. Ser. 6, 61-69 (1972; Zbl 246.10009)].
Classif.: * 11D04 Linear diophantine equations
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