A geometric approach to the diophantine Frobenius problem

Details A geometric approach to the diophantine Frobenius problem A geometric approach to the diophantine Frobenius problem

2010-07-12

arxiv.org/abs/1007.1840v1

Mathematics

Number Theory

12 pages, 5 figures, Plain TeX

Scientific paper

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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