07/11/13 03:22:28
Shapiro's Cyclic Inequality (google)
URLﾘﾝｸ(www.google.co.jp)
J. Ineq. Appl.
Shapiro’s cyclic inequality for even n (by P. J. Bushell and J. B. Mcleod)
URLﾘﾝｸ(www.hindawi.com)
In 1954 H. S. Shapiro proposed an inequality for a cyclic sum in n
variables. All the numerical evidence indicates that the inequality
is true for even n≤12 and for odd n≤23.
We give an analytic proof for the case n=12, which implies the former
result. The remaining case n=23 remains an open problem.
2002年の時点ではまだ未解決。