On a Linear Diophantine Problem of Frobenius
نویسنده
چکیده
Let a1, a2, . . . , ak be positive and pairwise coprime integers with product P . For each i, 1 ≤ i ≤ k, set Ai = P/ai. We find closed form expressions for the functions g(A1, A2, . . . , Ak) and n(A1, A2, . . . , Ak) that denote the largest (respectively, the number of) N such that the equation A1x1 + A2x2 + · · · + Akxk = N has no solution in nonnegative integers xi. This is a special case of the well-known Coin Exchange Problem of Frobenius.
منابع مشابه
The Frobenius Problem, Rational Polytopes, and Fourier-Dedekind Sums
where a1, . . . , an are positive integers. This polytope is closely related to the linear Diophantine problem of Frobenius: given relatively prime positive integers a1, . . . , an, find the largest value of t (the Frobenius number) such that m1a1 + · · · + mnan = t has no solution in positive integers m1, . . . , mn. This is equivalent to the problem of finding the largest dilate tP such that ...
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