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On a cyclic sum
Published online by Cambridge University Press: 18 May 2009
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1. For any positive integral n and any positive real x1,…,xn we write
clearly. It is known [1,2] that
for n ≦ 6, and further [4, 5, 6] that (5) is false for even n ≧ 14 and for odd n ≧ 53. Mordell [2] conjectured that (5) is false for all n ≧ 7, but recently [3] stated that computations indicated that (5) is true for n = 7 and gave some calculations in support of (5) for n = 7.
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- Copyright © Glasgow Mathematical Journal Trust 1963
References
REFERENCES
1.Diananda, P. H., Extensions of an inequality of H. S. Shapiro, Amer. Math. Monthly 66 (1959), 489–491.Google Scholar
2.Mordell, L. J., On the inequality 
and some others, Abh. Math. Sem. Univ. Hamburg 22 (1958), 229–240.CrossRefGoogle Scholar
and some others, Abh. Math. Sem. Univ. Hamburg 22 (1958), 229–240.CrossRefGoogle Scholar3.Mordell, L. J., Note on the inequality J. London Math. Soc. 37 (1962), 176–178.CrossRefGoogle Scholar
J. London Math. Soc. 37 (1962), 176–178.CrossRefGoogle Scholar5.Zulauf, A., Note on a conjecture of L. J. Mordell, Abh. Math. Sem. Univ. Hamburg 22 (1958), 240–241.Google Scholar
6.Zulauf, A., On a conjecture of L. J. Mordell, II, Math. Gaz. 43 (1959), 182–184.CrossRefGoogle Scholar
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