MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Federal Math Competition of Serbia and Montenegro
2002 Federal Math Competition of S&M
Problem 1
inequality with natural parameters
inequality with natural parameters
Source: S&M 2002 3&4th Grade P1
May 15, 2021
inequalities
Problem Statement
For any positive numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
and natural numbers
n
,
k
n,k
n
,
k
prove the inequality
a
n
+
k
b
n
+
b
n
+
k
c
n
+
c
n
+
k
a
n
≥
a
k
+
b
k
+
c
k
.
\frac{a^{n+k}}{b^n}+\frac{b^{n+k}}{c^n}+\frac{c^{n+k}}{a^n}\ge a^k+b^k+c^k.
b
n
a
n
+
k
+
c
n
b
n
+
k
+
a
n
c
n
+
k
≥
a
k
+
b
k
+
c
k
.
Back to Problems
View on AoPS