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arXiv · 1007.1840

A geometric approach to the diophantine Frobenius problem

Christian Blatter
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Abstract

It turns out that all instances of the diophantine Frobenius problem for three coprime a_i have a common geometric structure which is independent of arithmetic coincidences among the a_i. By exploiting this structure we easily obtain Johnson's formula for the largest non-representable z, as well as a formula for the number of such z. A procedure is described which computes these quantities in O(log(max a_i)) steps.

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Christian Blatter. 2010-07-12. A geometric approach to the diophantine Frobenius problem. https://arxiv.org/abs/1007.1840

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