Y by Adventure10, Mango247
A function
for all reals
satisfies a condition:
![\[ f(a,b,c)+f(b,c,d)+f(c,d,e)+f(d,e,a)+f(e,a,b)=a+b+c+d+e\]](//latex.artofproblemsolving.com/a/a/0/aa088a2aa8eda8ba15c7677317117a3e33394599.png)
Show that for all reals
(
) equality holds:
![\[ f(x_1,x_2,x_3)+f(x_2,x_3,x_4)+\ldots +f(x_{n-1},x_n,x_1)+f(x_n,x_1,x_2)=x_1+x_2+\ldots+x_n\]](//latex.artofproblemsolving.com/5/e/2/5e218537a98b731b36054f011fa254b35cdcaa5c.png)


![\[ f(a,b,c)+f(b,c,d)+f(c,d,e)+f(d,e,a)+f(e,a,b)=a+b+c+d+e\]](http://latex.artofproblemsolving.com/a/a/0/aa088a2aa8eda8ba15c7677317117a3e33394599.png)
Show that for all reals


![\[ f(x_1,x_2,x_3)+f(x_2,x_3,x_4)+\ldots +f(x_{n-1},x_n,x_1)+f(x_n,x_1,x_2)=x_1+x_2+\ldots+x_n\]](http://latex.artofproblemsolving.com/5/e/2/5e218537a98b731b36054f011fa254b35cdcaa5c.png)
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