Unbounded discrepancy in Frobenius numbers

Details Unbounded discrepancy in Frobenius numbers Unbounded discrepancy in Frobenius numbers

2010-02-26

arxiv.org/abs/1003.0021v2

Mathematics

Number Theory

this version solves one of the two open problems

Scientific paper

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.

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