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Some experimental results on the Frobenius problem. (English) Zbl 1076.11015

Based on experimental results it is conjectured \(g(a_1,a_2,a_3)\leq \sqrt{a_1a_2a_3}^{5/4}- a_1- a_2- a_3\), where \(g(a_1,a_2,a_3)\) is the Frobenius number in the case \(n= 3\).

MSC:

11D04 Linear Diophantine equations
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References:

[1] Ramirez Alfonsin J. L., The Diophantine Frobenius Problem. (2000)
[2] DOI: 10.1007/BF02574364 · Zbl 0804.52009 · doi:10.1007/BF02574364
[3] Beck Matthias, J. Number Theory 96 (1) pp 1– (2002)
[4] DOI: 10.2307/2371684 · Zbl 0061.06801 · doi:10.2307/2371684
[5] Brauer Alfred, J. Reine Angew. Math. 211 pp 215– (1962)
[6] DOI: 10.1006/jnth.1994.1071 · Zbl 0805.11025 · doi:10.1006/jnth.1994.1071
[7] Erdös P., Acta Arith. 21 pp 399– (1972)
[8] DOI: 10.4153/CJM-1960-033-6 · Zbl 0096.02803 · doi:10.4153/CJM-1960-033-6
[9] DOI: 10.1007/BF01204720 · Zbl 0753.11013 · doi:10.1007/BF01204720
[10] Knuth D. E., Acta Aritm. 33 pp 297– (1977)
[11] DOI: 10.1515/crll.1975.276.68 · Zbl 0305.10014 · doi:10.1515/crll.1975.276.68
[12] DOI: 10.2307/2320148 · Zbl 0424.10016 · doi:10.2307/2320148
[13] Rademacher H., Acta Arith. 9 pp 97– (1964)
[14] DOI: 10.1090/S0002-9939-1956-0091961-5 · doi:10.1090/S0002-9939-1956-0091961-5
[15] DOI: 10.1515/crll.1977.293-294.1 · Zbl 0349.10009 · doi:10.1515/crll.1977.293-294.1
[16] Sylvester J. J., Educational Times 41 pp 171– (1884)
[17] DOI: 10.1112/jlms/s2-10.1.79 · Zbl 0301.10020 · doi:10.1112/jlms/s2-10.1.79
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