MathDB

A function

f: R^3\rightarrow R

for all reals

a,b,c,d,e

satisfies a condition: f(a,b,c)\plus{}f(b,c,d)\plus{}f(c,d,e)\plus{}f(d,e,a)\plus{}f(e,a,b)\equal{}a\plus{}b\plus{}c\plus{}d\plus{}e Show that for all reals

x_1,x_2,\ldots,x_n

(

n\geq 5

) equality holds: f(x_1,x_2,x_3)\plus{}f(x_2,x_3,x_4)\plus{}\ldots \plus{}f(x_{n\minus{}1},x_n,x_1)\plus{}f(x_n,x_1,x_2)\equal{}x_1\plus{}x_2\plus{}\ldots\plus{}x_n

Problem Statement