**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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## Details

### 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*

### Abstract

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*.

### Keywords

*m*-representable- Frobenius number

### AMS Classification

- 11D04

### References

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## Cite this paper

APAChimni, 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.

ChicagoChimni, Sarthak, Soumya Sankar and Amitabha Tripathi. “On Integers that are Uniquely Representable by Modified Arithmetic Progressions.” Notes on Number Theory and Discrete Mathematics 22, no. 3 (2016): 36-44.

MLAChimni, Sarthak, Soumya Sankar and Amitabha Tripathi. “On Integers that are Uniquely Representable by Modified Arithmetic Progressions.” Notes on Number Theory and Discrete Mathematics 22.3 (2016): 36-44. Print.