On a cyclic sum
- 1 January 1963
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 6 (1) , 11-13
- https://doi.org/10.1017/s2040618500034626
Abstract
1. For any positive integral n and any positive real x1,…,xn we writeclearly. It is known [1,2] thatfor 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.Keywords
This publication has 6 references indexed in Scilit:
- Note on the Inequality ∑r=1nxr/(xr+1+xr+2) ⩾ ½nJournal of the London Mathematical Society, 1962
- 2850. On a conjecture of L. J. Mordell, II.The Mathematical Gazette, 1959
- Extensions of an Inequality of H. S. ShapiroThe American Mathematical Monthly, 1959
- On the inequality $$\sum\limits_{r = 1} {x_r /(x_{r + 1} + x_{r + 2} ) \geqslant n/2} $$ and some othersand some othersAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1958
- 2743. An inequalityThe Mathematical Gazette, 1958
- 2743. An inequalityThe Mathematical Gazette, 1958