MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Federal Math Competition of Serbia and Montenegro
2001 Federal Math Competition of S&M
Problem 3
Prime number ineq
Prime number ineq
Source: Serbian national cometition
April 11, 2014
inequalities
inequalities unsolved
Problem Statement
Let
p
1
,
p
2
,
.
.
.
,
p
n
p_{1}, p_{2},...,p_{n}
p
1
,
p
2
,
...
,
p
n
, where
n
>
2
n>2
n
>
2
, be the first
n
n
n
prime numbers. Prove that
1
p
1
2
+
1
p
2
2
+
.
.
.
+
1
p
n
2
+
1
p
1
p
2
.
.
.
p
n
<
1
2
\frac{1}{p_{1}^2}+\frac{1}{p_{2}^2}+...+\frac{1}{p_{n}^2}+\frac{1}{p_{1}p_{2}...p_{n}}<\frac{1}{2}
p
1
2
1
+
p
2
2
1
+
...
+
p
n
2
1
+
p
1
p
2
...
p
n
1
<
2
1
Back to Problems
View on AoPS