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