A note on the Frobenius and the Sylvester numbers

Amitabha Tripathi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 71–73
DOI: 10.7546/nntdm.2018.24.2.71-73
Full paper (PDF, 138 Kb)

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Authors and affiliations

Amitabha Tripathi
Department of Mathematics, Indian Institute of Technology
Hauz Khas, New Delhi – 110016, India

Abstract

Positive integers that cannot be represented by a linear form with relatively prime coefficients and over nonnegative integers are finite in number. We describe a connection between the largest number in this set and the cardinality of this set. We also describe a connection with a subset related to this set.

Keywords

• Representable
• Frobenius number

2010 Mathematics Subject Classification

• 11D07

References

1.  Nijenhuis, M. &Wilf, H. S. (1972) Representation of integers by linear forms in nonnegative integers, J. Number Theory, 4, 98–106.
2. Sylvester, J. J. (1884) Problem 7382, in W. J. C. Miller, ed., Mathematical Questions, with their Solutions, from the “Educational Times”, 41, 1884, p. 21. Solution by W. J. Curran Sharp.
3. Tripathi, A. (2003) On a variation of the Coin Exchange Problem for Arithmetic Progressions, Integers, 3, Article A01, 5 pages.