English

A geometric approach to the diophantine Frobenius problem

Number Theory 2010-07-13 v1

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.

Keywords

Cite

@article{arxiv.1007.1840,
  title  = {A geometric approach to the diophantine Frobenius problem},
  author = {Christian Blatter},
  journal= {arXiv preprint arXiv:1007.1840},
  year   = {2010}
}

Comments

12 pages, 5 figures, Plain TeX

R2 v1 2026-06-21T15:46:57.979Z