MATHEMATICA BOHEMICA, Vol. 133, No. 4, pp. 367-375 (2008)

On the Frobenius number of a modular
Diophantine inequality

J. C. Rosales, P. Vasco

J. C. Rosales, Departamento de Algebra, Universidad de Granada, E-18071 Granada, Spain, e-mail:; P. Vasco, Departamento de Matematica, Universidade de Tras-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal, e-mail:

Abstract: We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality $ax \mod b\leq x$, with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.

Keywords: numerical semigroup, Diophantine inequality, Frobenius number, multiplicity

Classification (MSC2000): 11D75, 20M14

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