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Costa Rica - Final Round
2003 Costa Rica - Final Round
3
3
Part of
2003 Costa Rica - Final Round
Problems
(1)
Cute inequality with integers
Source: Central American Olympiad 2003, Problem 3
5/23/2007
If
a
>
1
a>1
a
>
1
and
b
>
2
b>2
b
>
2
are positive integers, show that
a
b
+
1
≥
b
(
a
+
1
)
a^{b}+1 \geq b(a+1)
a
b
+
1
≥
b
(
a
+
1
)
, and determine when equality holds.
inequalities
induction
function
calculus