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Article overview
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Some experimental results on the Frobenius problem | Matthias Beck
; David Einstein
; Shelemyahu Zacks
; | Date: |
2 Apr 2002 | Journal: | Experimental Mathematics 12, no. 3 (2003), 263-269 | Subject: | Number Theory; Combinatorics MSC-class: 05A15, 11P21; 11Y16 | math.NT math.CO | Abstract: | We study the Frobenius problem: given relatively prime positive integers $a_1,...,a_d$, find the largest value of t (the Frobenius number) such that $sum_{k=1}^d m_k a_k = t$ has no solution in nonnegative integers $m_1,...,m_d$. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by $sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$. | Source: | arXiv, math.NT/0204036 | Services: | Forum | Review | PDF | Favorites |
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