MathDB
Problems
Contests
International Contests
Baltic Way
1996 Baltic Way
15
15
Part of
1996 Baltic Way
Problems
(1)
Find a,b for which cyclic x_i inequality holds
Source: Baltic Way 1998 Q15
3/19/2011
For which positive real numbers
a
,
b
a,b
a
,
b
does the inequality
x
1
x
2
+
x
2
x
3
+
…
x
n
−
1
x
n
+
x
n
x
1
≥
x
1
a
x
2
b
x
3
a
+
x
2
a
x
3
b
x
4
a
+
…
+
x
n
a
x
1
b
x
2
a
x_1x_2+x_2x_3+\ldots x_{n-1}x_n+x_nx_1\ge x_1^ax_2^bx_3^a+ x_2^ax_3^bx_4^a+\ldots +x_n^ax_1^bx_2^a
x
1
x
2
+
x
2
x
3
+
…
x
n
−
1
x
n
+
x
n
x
1
≥
x
1
a
x
2
b
x
3
a
+
x
2
a
x
3
b
x
4
a
+
…
+
x
n
a
x
1
b
x
2
a
hold for all integers
n
>
2
n>2
n
>
2
and positive real numbers
x
1
,
…
,
x
n
x_1,\ldots ,x_n
x
1
,
…
,
x
n
?
inequalities
inequalities proposed