Unbounded discrepancy in Frobenius numbers
Abstract
Let g_j denote the largest integer that is represented exactly j times as a nonnegative 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1003.0021
 Bibcode:
 2010arXiv1003.0021S
 Keywords:

 Mathematics  Number Theory;
 11D07;
 11D04;
 11D45
 EPrint:
 this version solves one of the two open problems