On integers that are uniquely representable by modified arithmetic progressions

Sarthak Chimni, Soumya Sankar and Amitabha Tripathi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 3, Pages 36—44
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Authors and affiliations

Sarthak Chimni
Department of Mathematics, Statistics, and Computer Science
The University of Illinois at Chicago
851 South Morgan Street, Chicago, IL 60607, USA

Soumya Sankar
Department of Mathematics, University of Wisconsin–Madison
Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, USA

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


For positive integers a, d, h, k, gcd(a, d) = 1, let A = {a, ha+d, ha+2d, …, ha+kd}. We characterize the set of nonnegative integers that are uniquely representable by nonnegative integer linear combinations of elements of A.


  • m-representable
  • Frobenius number

AMS Classification

  • 11D04


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Cite this paper

Chimni, S., Sankar, S. & Tripathi, A. (2016). On integers that are uniquely representable by modified arithmetic progressions, Notes on Number Theory and Discrete Mathematics, 22(3), 36-44.

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