MathDB
Problems
Contests
National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
2013 Spain Mathematical Olympiad
1
1
Part of
2013 Spain Mathematical Olympiad
Problems
(1)
Inequality
Source: Spanish Mathematical Olympiad. 2013. Problem 1
3/26/2015
Let
a
,
b
,
n
a,b,n
a
,
b
,
n
positive integers with
a
>
b
a>b
a
>
b
and
a
b
−
1
=
n
2
ab-1=n^2
ab
−
1
=
n
2
. Prove that
a
−
b
≥
4
n
−
3
a-b \geq \sqrt{4n-3}
a
−
b
≥
4
n
−
3
and study the cases where the equality holds.
inequalities