Unbounded discrepancy in Frobenius numbers
Number Theory
2010-09-08 v2
Abstract
Let g_j denote the largest integer that is represented exactly j times as a non-negative integer linear combination of { x_1, ... , x_n. We show that for any k > 0, and n = 5, the quantity g_0 - g_k is unbounded. Furthermore, we provide examples with g_0 > g_k for n >= 6 and g_0 > g_1 for n >= 4.
Keywords
Cite
@article{arxiv.1003.0021,
title = {Unbounded discrepancy in Frobenius numbers},
author = {Jeffrey Shallit and James Stankewicz},
journal= {arXiv preprint arXiv:1003.0021},
year = {2010}
}
Comments
this version solves one of the two open problems