Geodesic
The Frobenius Problem for Classes of Polynomial Solvability
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 845-853.

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The Frobenius problem is to find a method ($=$ algorithm) for calculating the largest “sum of money” that cannot be given by coins whose values $b_0,b_1,\dots,b_w$ are coprime integers. As admissible solutions (algorithms), it is common practice to study polynomial algorithms, which owe their name to the form of the dependence of time expenditure on the length of the original information. The difficulty of the Frobenius problem is apparent from the fact that already for $w=3$ the existence of a polynomial solution is still an open problem. In the present paper, we distinguish some classes of input data for which the problem can be solved polynomially; nevertheless, argumentation in the spirit of complexity theory of algorithms is kept to a minimum. 
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I. D. Kan. The Frobenius Problem for Classes of Polynomial Solvability. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 845-853. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a3/

[1] Shevchenko V. N., Kachestvennye voprosy tselochislennogo programmirovaniya, Nauka, M., 1995 | Zbl

[2] Johnson S. M., “A linear diophantine problem”, Canad. J. Math., 12:2 (1960), 390–398 | MR | Zbl

[3] Rödset Ö. J., “On a linear diophantine problem of Frobenius, II”, J. Reine Angew. Math., 307/308 (1979), 431–440 | MR | Zbl

[4] Kan I. D., “Predstavlenie chisel lineinymi formami”, Matem. zametki, 68:2 (2000), 210–216 | MR | Zbl

[5] Kan I. D., “K probleme Frobeniusa”, Fundamentalnaya i prikladnaya matematika, 3:3 (1997), 821–835 | MR | Zbl

[6] Brauer A., Shockly J. E., “On a problem of Frobenius”, J. Reine Angew. Math., 211:3/4 (1962), 215–220 | MR | Zbl

[7] Lenstra H. W., “Integer programming with a fixed number of variables”, Math. of Oper. Res., 8:4 (1983), 538–548 | DOI | MR | Zbl

[8] Kai-Man Tsang, “On a linear diophantine problem of Frobenius”, Studia Scientarum Math. Hungarica, 23 (1988), 443–452 | MR

[9] Selmer E. S., “On the linear diophantine problem of Frobenius”, J. Reine Angew. Math., 293/294 (1977), 1–17 | MR | Zbl