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On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
-
Amitabha Tripathi
Published/Copyright:
November 5, 2010
Abstract
For positive integers a, k, let denote the sequence ak, ak + 1, ak + a, . . . , ak + ak−1. Let
denote the set of integers that are expressible as a linear combination of elements of
with non-negative integer coefficients. We determine
and
which denote the largest (respectively, the number of) positive integer(s) not in
. We also determine the set
of positive integers not in
which satisfy
, where
=
\ {0}.
Keywords.: Representable; Frobenius number
Received: 2009-11-14
Revised: 2010-05-07
Accepted: 2010-05-13
Published Online: 2010-11-05
Published in Print: 2010-November
© de Gruyter 2010
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Articles in the same Issue
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
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