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On a cyclic sum

Published online by Cambridge University Press:  18 May 2009

P. H. Diananda
P. H. Diananda
Affiliation:
Department of MathematicsUniversity of Singapore
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 1 , January 1963 , pp. 11 - 13
Copyright
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
3.Mordell, L. J., Note on the inequality J. London Math. Soc. 37 (1962), 176–178.CrossRefGoogle Scholar
4.Rankin, R. A., An inequality, Math. Gaz. 42 (1958), 39–40.CrossRefGoogle Scholar
5.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