On the Frobenius number of a modular Diophantine inequality
Mathematica Bohemica (2008)
- Volume: 133, Issue: 4, page 367-375
- ISSN: 0862-7959
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topRosales, José Carlos, and Vasco, P.. "On the Frobenius number of a modular Diophantine inequality." Mathematica Bohemica 133.4 (2008): 367-375. <http://eudml.org/doc/250542>.
@article{Rosales2008,
abstract = {We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality $ax ~\@mod \;b\le x$, with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.},
author = {Rosales, José Carlos, Vasco, P.},
journal = {Mathematica Bohemica},
keywords = {numerical semigroup; Diophantine inequality; Frobenius number; multiplicity; numerical semigroup; Diophantine inequality; Frobenius number; multiplicity},
language = {eng},
number = {4},
pages = {367-375},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Frobenius number of a modular Diophantine inequality},
url = {http://eudml.org/doc/250542},
volume = {133},
year = {2008},
}
TY - JOUR
AU - Rosales, José Carlos
AU - Vasco, P.
TI - On the Frobenius number of a modular Diophantine inequality
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 4
SP - 367
EP - 375
AB - We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality $ax ~\@mod \;b\le x$, with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
LA - eng
KW - numerical semigroup; Diophantine inequality; Frobenius number; multiplicity; numerical semigroup; Diophantine inequality; Frobenius number; multiplicity
UR - http://eudml.org/doc/250542
ER -
References
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- Rosales, J. C., Modular Diophantine inequalities and some of their invariants, Indian J. Pure App. Math. 36 (2005), 417-429. (2005) Zbl1094.20037MR2199217
- Rosales, J. C., García-Sánchez, P. A., Finitely Generated Commutative Monoids, Nova Science Publishers, New York (1999). (1999) MR1694173
- Rosales, J. C., García-Sánchez, P. A., a-García, J. I. Garcí, Urbano-Blanco, J. M., 10.1016/j.jnt.2003.06.002, J. Number Theory 103 (2003), 281-294. (2003) MR2020273DOI10.1016/j.jnt.2003.06.002
- Rosales, J. C., García-Sánchez, P. A., Urbano-Blanco, J. M., 10.2140/pjm.2005.218.379, Pacific J. Math. 218 (2005), 379-398. (2005) Zbl1184.20052MR2218353DOI10.2140/pjm.2005.218.379
- Rosales, J. C., Urbano-Blanco, J. M., 10.1016/j.jalgebra.2006.08.009, J. Algebra 306 (2006), 368-377. (2006) Zbl1109.20052MR2271340DOI10.1016/j.jalgebra.2006.08.009
- Rosales, J. C., Vasco, P., The smallest positive integer that is solution of a proportionally modular Diophantine inequality, Math. Inequal. Appl. 11 (2008), 203-212. (2008) Zbl1142.20042MR2410272
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