Geodesic
On a special case of the Frobenius problem
Journal of integer sequences, Tome 20 (2017) no. 7
For any set of positive and relatively prime integers $A$, the set of positive integers that are not representable as a nonnegative integral linear combination of elements of $A$ is always a non-empty finite set. Thus we may define $g(A), n(A), s(A)$ to denote the largest integer in, the number of integers in, and the sum of integers in this finite set, respectively. We determine $g(A), n(A), s(A)$ when $A = {a, b, c}$ with $a | lcm(b, c)$. A particular case of this is when $A = {kl, lm, mk}$, with $k, l, m$ pairwise coprime. We also solve a related problem when $a | lcm(b, c)$, thereby providing another proof of the formula for $g(A)$.
Classification : 11D07
Keywords: linear Diophantine equation, Frobenius problem 
@article{JIS_2017__20_7_a2,
     author = {Tripathi,  Amitabha},
     title = {On a special case of the {Frobenius} problem},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {7},
     zbl = {1366.11057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a2/}
}
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Tripathi,  Amitabha. On a special case of the Frobenius problem. Journal of integer sequences, Tome 20 (2017) no. 7. http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a2/