A formula for the number of non-negative integer solutions of a1x1 + a2x2 + ··· + amxm = n in terms of the partial Bell polynomials

Sumit Kumar Jha
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 64—69
DOI: 10.7546/nntdm.2021.27.2.64-69
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Sumit Kumar Jha
International Institute of Information Technology
Hyderabad-500 032, India

Abstract

We derive a formula for the number of non-negative integer solutions of the equation a_1x_1 + a_2x_2 + \cdots + a_mx_m = n in terms of the partial Bell polynomials via the Faa di Bruno’s formula.

Keywords

  • Linear Diophantine equation
  • Generating function

2020 Mathematics Subject Classification

  • 11D45
  • 05A15

References

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Cite this paper

Jha, S. K. (2021). A formula for the number of non-negative integer solutions of a1x1 + a2x2 + ··· + amxm = n in terms of the partial Bell polynomials. Notes on Number Theory and Discrete Mathematics, 27(2), 64-69, doi: 10.7546/nntdm.2021.27.2.64-69.

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