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The Frobenius Problem for Modified Arithmetic Progressions
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Amitabha Tripathi

Department of Mathematics

Indian Institute of Technology

Hauz Khas, New Delhi – 110016

India

**Abstract:**

For a set of positive and relative prime integers *A*,
let Γ(*A*) denote the
set of integers obtained by taking all nonnegative integer linear
combinations of integers in *A*. Then there are finitely many positive
integers that do not belong to Γ(*A*). For the modified arithmetic
progression *A* = {*a*, *ha* + *d*, *ha* + 2*d*, ... , *ha* + *kd*}, gcd(*a*, *d*) = 1, we
determine the largest integer **g**(*A*) that does not belong to
Γ(*A*), and the
number of integers **n**(*A*) that do not belong to
Γ(*A*). We also determine
the set of integers S*(*A*) that do not belong to Γ(*A*)
which, when added to
any positive integer in Γ(*A*), result in an integer in
Γ(*A*). Our results
generalize the corresponding results for arithmetic progressions.

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Received May 15 2013;
revised version received July 31 2013.
Published in *Journal of Integer Sequences*, August 1 2013.

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